Bhagya

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Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 4 Geometry Additional Questions

Additional Questions and Answers

Exercise 4.1

Question 1.
“The sum of any two angles of a triangle is always greater than the third angle”. Is this statement true. Justify your answer.
Solution:
No, the sum of any two angles of a triangle is not always greater than the third angle. In an isosceles right angled triangles, the angle will be 90°, 45°, 45°.
Here sum of two angles 45° + 45° = 90°.

Question 2.
The three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle. Classify the triangle in two different ways.
Solution:
Let the angles of the triangle be x, 2x, x.
Using the angle sum property, we have
x + 2x + x = 180°
4x = 180°
x = \(\frac{180^{\circ}}{4}\)
x = 45°
2x = 2 × 45° = 90°
Thus the three angles of the triangle are 45°, 90°, 45°.
Its two angles are equal. It is an isoscales triangle. Its one angle is 90°.
∴ It is a right angled triangle.

Question 3.
Find the values of the unknown x and y in the following figures

Solution:
(i) Since angles y and 120° form a linear pair.
y + 120° = 180°
y = 180° – 120°
y = 60°
Now using the angle sum property of a triangle, we have
x + y + 50° = 180°
x + 60° + 50° = 180°
x + 110° = 180°
x = 180° – 110°= 70°
x = 70°
y = 60

(ii) Using the angle sum property of triangle, we have
50° + 60° + y = 180°
110° + y = 180°
y = 180° – 110°
y = 70°
Again x and y form a linear pair
∴ x + y = 180°
x + 70° = 180°
x = 180° – 70°= 110°
∴ x = 110°; y = 70°

Question 4.
Two angles of a triangle are 30° and 80°. Find the third angle.
Solution:
Let the third angle be x.
Using the angle sum property of a triangle we have,
30° + 80° + x = 180°
x + 110° = 180°
x = 180° – 110° = 70°
Third angle = 70°.

Exercise 4.2

Question 1.
In an isoscleles ∆ABC, AB = AC. Show that angles opposite to the equal sides are equal.
Solution:

Given: ∆ABC in which \(\overline{A B}\) = \(\overline{A C}\).
To Prove: ∠B = ∠K.
Construction: Draw AD ⊥ BC.
Proof: In right ∆ADB and right ∆ADC.
we have side AD = side AD (common)
AB = AC (Hypoteneous) (given)
∆ADB = ADC (RHS criterion]
∴ Their corresponding parts are equal. ∠B = ∠C.

Question 2.
ABC is an isosceles triangle having side \(\overline{A B}\) = side \(\overline{A C}\). If AD is perpendicular to BC, prove that D is the mid-point of \(\overline{B C}\).
Solution:
In ∆ABD and ∆ACD, we have
∠ADB = ∠ADC [∵ AD ⊥ BC]
Side \(\overline{A D}\) = Side \(\overline{A D}\) [Common]
Side \(\overline{A B}\) = Side \(\overline{A C}\) [Common]
Using RHS congruency, we get
∆ABD ≅ ∆ACDc
Their corresponding parts are equal

∴ BD = CD
∴ O is the mid point of BC.

Question 3.
In the figure PL ⊥ OB and PM ⊥ OA such that PL = PM.
Prove that ∆PLO ≅ ∆PMO.
Solution:

In ∆PLO and ∆PMO, we have
∠PLO = ∠PMO = 90° [Given]
\(\overline{O P}\) = \(\overline{O P}\) [Hypotenuse]
PL = PM
Using RHS congruency, we get
∆PLO ≅ ∆PMO

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Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.2

Question 1.
Complete the Pascal’s Triangle.

Solution:

Question 2.
The following hexagonal shapes are taken from Pascal’s Triangle. Fill in the missing numbers.

Solution:

Question 3.
Complete the Pascal’s Triangle by taking the numbers 1,2,6,20 as line of symmetry.

Solution:
Corresponding numbers are equal about the line of symmetry.

Objective Type Questions

Question 1.
The elements along the sixth row of the Pascal’s Triangle is
(i) 1,5,10,5,1
(ii) 1,5,5,1
(iii) 1,5,5,10,5,5,1
(iv) 1,5,10,10,5,1
Answer:
(iv) 1,5,10,10,5,1

Question 2.
The difference between the consecutive terms of the fifth slanting row containing four elements of a Pascal’s Triangle is
(i) 3,6,10,…
(ii) 4,10,20,…
(iii) 1,4,10,…
(iv) 1,3,6,…
Answer:
(ii) 4,10,20,…

Question 3.
What is the sum of the elements of ninth row in the Pascal’s Triangle?
(i) 128
(ii) 254
(iii) 256
(iv) 126
Answer:
(iii) 256

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Tamilnadu Samacheer Kalvi 12th English Expand the News Headlines

1. Saina Receives Khel Ratna Award
New Delhi: Badminton ace Saina Nehwal, whose phenomenal rise was highlighted by three top-flight international titles, recently, was on Sunday conferred the coveted Rajiv Gandhi Khel Ratna award at a glittering ceremony here on Sunday. Saina’s achievements in the past one year made her an automatic choice for the prestigious award, the highest sporting honour in the country.

2. Forgotten Brother Appears
Jharkhand: A forgotten brother has appeared after a long period of time.Mr.Ranjan and Mr. Anjan were reunited after the latter went missing in a Mela at Jharkand. They are united after 43 long years. Mr. Ranjan was taken care of by a local NGO and has a success story to narrate.

3. Maid Wins Maruti Car as Prize
Trichy: The fortune of a house-maid today changed when she won Maruti car as a prize in the local mela raffle. As she has no one to drive the car in her family, she decided to sell it. However, Mr. Ramakrishnan in whose house she works as a house maid, suggested that she rents it out to earn an extra amount for her family.

4. Crores Approved
Trichy:The municipality has launched a comprehensive drive, at a cost of Rs. 1.41 crore, to clean drainage-canal-tumed irrigation canals, meandering through the town, ahead of the Mahamaham festival.The effort would provide a fresh lease of life to five canals that were once irrigation channels but over the decades got transformed into drainage channels. A lot of development works were being undertaken; the town was being given a facelift ahead of the festival.Public sanitation has been accorded priority, she added.

5. Passerby Sees Woman Jump
ChennaiiA passerby reportedly stopped a woman from jumping off a pedestrian bridge at the Kotturpuram bus stop on Saturday. It is understood that some family duel is the reason for her drastic decision. The woman climbed over the guardrail and sat on it. Some passersby joined hands and forced her to come down.Suicidal Prevention Centre was informed.

6. Difficult Times Ahead
New Delhi: The Finance Minister has predicted difficult times for the Indian Economy in the years ahead. As he enters the final year of the government’s term, he is probably facing as many – if not more – economic problems as he did when he took charge. In fact, one would say if the BJP returns to power, Prime Minister Modi will have to work even harder than he did in his first term to keep the economy on an even keel.

7. Professors Protest Pay Cuts
New Delhi: Days after warning them, the administration of the Jawaharlal Nehru University (JNU) has decided to deduct the salaries of the teachers for participating in protests. The teachers protested against the administration’s decision to scrap the old recruitment and admission policy as well as the multiple show-cause notices against students and teachers. The university’s administration has banned any kind of protest within 20 meters of the building.

8. Tommy The Dog Named Hero
New Delhi: Tommy,the popular dog from Chennai was declared the hero at The Canine Meet held at Delhi. The owner Vijay Prabhakar, says that he has hired Dog trainers from far and wide to train his dogs and this is the second National award for Tommy. Tommy is expected to take part in the International Canine meet in 2020.

9. President Declares Celebration
Mumbai: The President of India, Shri Ram NathKovind, graced and addressed a function organised to declare urban Maharashtra Open. He also inaugurated the centenary year celebrations of the Samadhi of Shri Sai Baba in Shirdi. He was felicitated by the local party members.

10. Security Alert In Bhopal
Bhopal: In the city of Bhopal, after receiving two anonymous calls, police department is on the alert day and night.Bhopal is on the radar of the terrorist outfits. Taking serious note of the intelligence given previously, the State police headquarters has sounded a high alert in the city.

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Tamilnadu Samacheer Kalvi 9th Science Solutions Chapter 16 Applied Chemistry

Samacheer Kalvi 9th Science Applied Chemistry Textbook Exercises

I. Choose the correct answer.

Question 1.
One Nanometre is ………………
(a) 10^{– 7} metre
(b) 10^{– 8} metre
(c) 10^{– 6} metre
(d) 10^{– 9} metre
Answer:
(d) 10^{– 9} metre

Question 2.
The antibiotic Penicillin is obtained from …………………
(a) plant
(b) microorganism
(c) animal
(d) sunlight
Answer:
(b) microorganism

Question 3.
1 % solution of Iodoform is used as ……………..
(a) antipyretic
(b) antimalarial
(c) antiseptic
(d) antacid
Answer:
(c) antiseptic

Question 4.
The cathode of an electrochemical reaction involves …………….
(a) oxidation
(b) reduction
(c) neutralisation
(d) catenation
Answer:
(b) reduction

Question 5.
The age of a dead animal can be determined by using an isotope of ………………..
(a) carbon
(b) iodine
(c) phosphorous
(d) oxygen
Answer:
(a) carbon

Question 6.
Which of the following does not contain natural dyes?
(a) Potato
(b) Beetroot
(c) Carrot
(d) Turmeric
Answer:
(a) Potato

Question 7.
This type of food protect us from deficiency diseases.
(a) Carbohydrates
(b) Vitamins
(c) Proteins
(d) Fats
Answer:
(b) Vitamins

Question 8.
Radiochemistry deals with ……………….
(a) oxidants
(b) batteries
(c) isotopes
(d) nanoparticles
Answer:
(c) isotopes

Question 9.
The groups responsible for the colour of an organic compound is called ………………….
(a) isotopes
(b) auxochrome
(c) chromogen
(d) chromophore
Answer:
(d) chromophore

Question 10.
Chlorinated hydrocarbons are used as ……………..
(a) fertilizers
(b) pesticides
(c) food colourants
(d) preservatives
Answer:
(b) pesticides

II. Fill in the blanks.

1. ……………. is an electrochemical cell which converts electrical energy into chemical change (Reaction).
2. Painkiller drugs are called ……………..
3. Aspirin is an …………….
4. …………. , …………….. and …………… are macronutrients required for plant growth.
5. ……………. is a chemical used in fingerprint analysis.

Answer:

1. Electrolytic cell
2. Analgesic
3. Analgesics
4. Nitrogen, Phosphorous, Potassium
5. Ninhydrin

III. Match the following.

S.No.	A	B
1.	Antipyretics	(a) Large surface area
2.	Corrosion prevention	(b) Iodine-131
3.	Hyperthyroidism	(c) Fever
4.	Nanoparticle	(.d) Cancer cell identification
5.	Nanorobotics	(e) Electroplating

Answer:

1. (c) Fever
2. (e) Electroplating
3. (b) Iodine – 131
4. (a) Large surface area
5. (d) Cancer cell identification

IV. Answer in brief.

Question 1.
What is Chemotherapy?
Answer:
Treatment of certain diseases by destroying the invading organism without damaging the cells of the host, by the use of certain organic compounds is known as Chemotherapy.

Question 2.
What is called Anaesthetics? How are they classified?
Answer:
The drugs which cause loss of sensation are called Anaesthetics.
Classification: Anaesthetics are classified according to the area of application as,

• General Anaesthetics,
• Local Anaesthetics.

Question 3.
What is the need for chemical fertilizers in crop fields?
Answer:
Chemical fertilizers provide the essential micro and macronutrients for crop growth that may not be sufficiently available in the soil.

Question 4.
What is Forensic chemistry related to?
Answer:
Forensic chemistry is related to the application of scientific principles, techniques, and methods to the investigation of crime.

V. Answer in detail.

Question 1.
Explain the types of dyes based on their method of application.
Answer:
1. Acid Dyes

• These are acidic in nature.
• They are used for dyeing animal fibres and synthetic fibres.
• These can be used for protein fibre such as wool and silk.
  Example: Picric acid, Naphthol yellow-s

2. Basic Dyes:

• These are basic dyes containing basic group (- NH₂, NHR, -NR₂).
• They are used for dyeing animal fibres and plant fibres.
  (Example: Crystal violet, Methylene Blue).

3. Mordant dyes (or) Indirect Dyes :

• These dyes have a poor affinity for cotton fabrics and hence do not dye directly.
• They require pretreatment of the fibre with a mordant.
• Mordant is a substance which can be fixed to the fibre and then can be combined with the dye to form an insoluble complex called lake. Salts of aluminium, chromium and iron are used as mordants.
  Example: Alizarin.

4. Direct Dyes:

• They have high affinity for cotton, rayon and other cellulose fibre.
• So they are applied directly as they fix firmly on the fabric.
  Example: Congo red.

5. Vat Dyes:

• It can be used only on cotton and, not on silk and wool.
• This dyeing is a continuous process and is carried out in a large vessel called vat.
• So it is called a Vat dye.
  Example: Indigo

Question 2.
Name various food additives and explain their functions.
Answer:

Type of additive	The function of the additive	Example
Preservatives	They protect food from spoilage by microorganisms in storage.	Vinegar, Sodium benzoate, benzoic acid, sodium nitrite
Colourants	They give pleasant colours to food	Carotenoids, Anthocyanin, Curcumin
Artificial Sweeteners	They add sweet taste to food	Saccharin, Cyclamate
Flavor enhancers	They are used to enhance the flavor of food items	Monosodium glutamate, Calcium diglutamate
Antioxidants	They prevent the oxidation of food. They protect us against cardiovascular disease.	Vitamin C, Vitamin E, Carotene

VI. HOTS

Question 1.
Batteries that are used in the mobile phones can be recharged. Likewise, can you recharge the batteries used in watches? Justify your answer.
Answer:
A primary cell cannot be recharged. Watch batteries have a primary cell. In a primary cell, chemical energy is converted into electrical energy when current is drawn from it.

Whereas mobile phones use secondary cells. In secondary cells, electrical energy is converted to chemical energy when current is passed through it and chemical energy is converted to electrical energy when current is drawn from it.

Question 2.
Sudha met with a fire accident. What kind of drug(s), she must take?
Answer:

• Antibiotic ointments must be used to treat the bums.
• Analgesic tablets can be taken to relieve pain.
• Antiseptic creams can be given to prevent infection.

Question 3.
The soil pH of cropland is 5. What kind of fertilizers should be used in that land?
Answer:
Organic fertilizer like compost can be used to maintain pH of soil at 6.5, which is ideal for soil and to moderate the acidity.

Samacheer Kalvi 9th Science Applied Chemistry Additional Questions

I. Answer briefly.

Question 1.
Explain the structure of an electrolytic cell.
Answer:

• It is an electrochemical cell which converts electrical energy into chemical energy i.e. in electrolytic cells, electricity is used to bring about chemical reactions.
• Here, both anode and cathode are in contact with Anode same electrolyte and thus the half-cells are not separated. As seen in galvanic cells, the electrolytic cell also involves redox reaction. We get electricity from galvanic cells. But electrolytic cells use electricity.
• In electrolytic cells, when electricity is passed to the electrolyte, it dissociates into its constituent ions. These ions undergo redox reactions forming the respective elements. This phenomenon is called Electrolysis. So electrolysis is a process by which an electrolyte is decomposed into its constituent elements by passing electricity through its aqueous solution or fused (molten) state.

Question 2.
How does galvanic cells produce electricity?
Answer:
In a galvanic cell, at anode oxidation takes place which releases electrons. These electrons are attracted by the cathode and hence the electrons flowing from anode to cathode are gained in the reduction reaction. As long as the redox reaction proceeds, there is a flow of electrons and hence electricity.

Question 3.
What are drugs? What are their characteristics?
Answer:
The chemicals used for treating diseases are termed as drug.
Characteristics of drugs: A drug must possess the following;

1. It should not be toxic
2. It should not cause any side effects.
3. It should not affect the receptor tissue
4. It should not affect the normal physiological activities
5. It should be effective in its action.

Question 4.
Write the applications of Nanochemistry.
Answer:
Some applications of Nanochemistry are:

1. The metallic nanoparticles can be used as very active catalysts.
2. Chemical sensors from nanoparticles and nanowires enhance the sensitivity and sensor selectivity.
3. Nanocoatings and nanocomposites are found useful in making a variety of products such as sports equipment, bicycles and automobiles etc.
4. These are used as novel UV-blocking coatings on glass bottles which protect beverages from being damaged by sunlight.
5. Nanotechnology is being applied in the production of synthetic skin and implant surgery.
6. Nanomaterials that conduct electricity are being used in electronics as minute conductors to produce circuits for microchips.
7. Nanomaterials have extensive applications in the preparation of cosmetics, deodorants and sunscreen lotion and they are used to improve moisturizers without making them too oily.
8. Nanoparticle substances are incorporated in fabrics to prevent the growth of bacteria.
9. Biomedical devices like drug infusion pumps, microneedles and glucometers are made from nanomaterials.
10. Nanochemistry is used in making space, defence and aeronautical devices

Question 5.
What are the applications of Radiochemistry?
Answer:
Important applications of radioisotopes are as under –

• Radiocarbon dating – its a method by which the age of fossil wood or animal is determined using C-14 isotope.
• Study of chemical reactions – the nature of some chemical reactions can be studied by mixing a radioisotope with a non-radioactive isotope of the reactants. The radioisotope used for this purpose is radiotracer.
• Diagnosis – Radioisotope is found very useful to diagnose and understand many diseases.

Question 6.
Write a note on Natural dyes.
Answer:
Many natural dyes have been known from a long time. These are obtained from vegetable sources.

• Henna: It is a reddish-brown dye obtained from plant Lawsonia inermis (Tamil: Maruthondri). A paste of these leaves is used as a hair dye and also for colouring palms.
• Turmeric: It is the traditional natural cosmetic in India. It is obtained from the plant Curcuma. longa. It also acts as an antiseptic. Turmeric is mostly used in India for colouring food.

Question 7.
What is electroplating? Why is it done?
Answer:
The process of depositing a thin layer of one metal over another metal by the process of electrolysis is called electroplating.
It is done to protect the metal from corrosion. For example, metals like iron are electroplated with tin, nickel, or chromium to protect them from rusting.

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Tamilnadu Samacheer Kalvi 9th English Vocabulary Idioms

An idiom is an expression in English with a special meaning of its own. Idioms do not give the literal meaning of the individual words used in them.

Here are a few sentences with idioms (meanings are given in brackets):

• Business is going from bad to worse, (deteriorate further)
• They always do things in a big way, (on a large scale)
• The government has taken a very hard line (not giving in) against illegal quarrying.
• Orders for the new product are coming in thick and fast, (in large numbers)
• How can any one make ends meet (manage with the money) with just ? 2000/- a month?
• Your son’s behavior is a matter of concern, (something to worry about)
• The name sounds familiar but I can’t call her face to mind, (recall something from memory; recognise)
• My uncle loves to tell us how to play cricket. He is an armchair expert.
  (one who gives advice in an area in which he was not actively involved)
• Ravi is our sincere employee. He has had a clean slate (a past record without discredit) for over twenty years.
• The policeman went near the damaged car to have a look at close quarters, (very near)
• Dr. Jacob is at the helm (in charge) of affairs in this hospital.
• No one can make a break even (make no profit or loss) in the first year of business.
• Because of the steep rice in prices, people living on pension feel the pinch, (feeling unpleasant change in one’s standard of living)
• Let us settle the bill for the damage fair and square, (in a fair way)
• I can hear you over phone loud and clear, (very clearly)
• By and by (as time goes by) he will realise that my going to Delhi was the right decision.

Idioms from the Textual Exercises
Idiom – Meaning
1. alarm bells ringing – a sign of something going wrong
2. back to the wall – in serious difficulty
3. below the belt – unfair or unsporting behavior
4. by the skin of one’s teeth – a narrow escape.
5. drive one up the wall – to annoy or irritate someone
6. asp / clutch at straws – try any method to overcome a crisis
7. hang out to dry – abandoning one who is in difficulty
8. have cold feet – feel nervousness and anxiety
9. hit the road – to begin one’s journey
10. in a nice pickle – in a troublesome or difficult situation
11. in our corner – on your side in an argument or dispute
12. in panic mode – in a frightening state
13. on the ropes – state of near collapse or defeat
14. right up to one’s alley – ideally suited to one’s interest
15. saved by the bell – help at the last moment rescuing one from a difficult situation
16. shot his bolt – to exhaust one’s effort
17. square off – prepare for a conflict
18. take (one) for a ride – to deceive someone
19. throw in the towel – to give up
20. tight corners – difficult situations

Some more idioms and meanings :

1	a bolt from the blue	unexpected event; complete surprise (usually unwelcome)
2	a drop in the ocean	a very small amount compared with what is needed or expected
3	a great deal	plenty of
4	a penny for your thoughts	a way of asking what someone is thinking.
5	a stone’s throw	a very short distance
6	a storm in a teacup	a big fuss about a small problem
7	a wild goose chase	a worthless hunt or chase
8	a yellow streak	cowardice in one’s character
9	above board	honest, not a secret
10	add insult to injury	to worsen an unfavorable situation
11	armchair expert	one who gives advice in an area in which he was not actively involved
12	at close quarters	very near
13	at hand	very near
14	at loggerheads	to disagree strongly
15	at snail’s pace	very slowly
16	at the drop of the hat	without any hesitation
17	at the eleventh hour	at the last moment
18	at the end of one’s tether	to have no power, patience or endurance left
19	at the helm	in charge
20	at the mercy of	under the control of
21	barking up the wrong tree	accusing the wrong person
22	be armed with	be equipped with
23	be fit for	suitable
24	be part of	belong to
25	beat around the bush	avoiding the main topic
26	bed of roses	comfortable position
27	best of both worlds	all the advantages
28	big way	on a large scale
29	bite the bullet	to get something over with because it is inevitable
30	blessing in disguise	something good that isn’t recognized at first.
31	bolt from the blue	something that happened without warning
32	break even	make no profit or loss
33	break the ice	make people feel more comfortable
34	break through	penetrate
35	bring forth	produce
36	burst into	enter suddenly
37	by and by	as time goes by
38	by nature	because of natural habits
39	call it a day	stop working on something
40	can’t judge a book by its cover	cannot judge something primarily on appearance.
41	clean slate	a past record without discredit
42	comparing apples to oranges	comparing two things that cannot be compared
43	costs an arm and a leg	very expensive
44	curiosity killed the cat	being inquisitive can lead you into an unpleasant situation.
45	devil’s advocate	to present a counter argument
46	draw a blank	unable to get information
47	every cloud has a silver lining	good-things come after bad things
48	eyesore	ugly sight
49	eyewash	something to deceive
50	fair and square	in a fair way
51	fall a prey to	become a victim
52	far cry from	very different from
53	far from	distant
54	feel the pinch	feeling unpleasant change in one’s standard of living
55	fit as a fiddle	in good health
56	fortune favours the bold	take risks
57	give (someone) a piece of one’s mind	to tell someone frankly what one thinks especially when one disapproves of the other’s behaviour
58	give someone the cold shoulder	ignore someone
59	go down in flames	fail spectacularly
60	go on a wild goose chase	to do something pointless
61	going from bad to worse	deteriorate further
62	good-for-nothing	worthless
63	hang around	someone strongly to loiter
64	hang in there	don’t give up
65	hard to come by	difficult to find
66	have a hand	to get involved
67	have no hand in	does not take part in an activity
68	head back	return
69	herculean task	difficult task
70	hit the nail on the head	do or say something exactly right
71	hit the sack	go to sleep
72	holds good	valid at the time of discussion
73 ,	honour bound (to do something)	required to do something as a moral duty but not by law
74	in a nutshell	briefly
75	in all walks of life	all social groups
76	in deep waters	in trouble
77	in hot pursuit	following closely
78	in short supply	Not enough / scarce
79	in the hands of	in the care of
80	in the service of	available for
81	it is a piece of cake	it is easy
82	it’s Taining cats and dogs	it’s raining hard
83	keep pace with	to move with same speed
84	keep something at bay	keep something away
85	kicked the bucket	passed away
86	leave no stone unturned	look everywhere
87	let the cat out of the bag	give away a secret
88	lion’s share	major share
89	look down upon	treat with contempt                        .
90	loud and clear	very clearly
91	make both ends meet	live within means
92	make fun of	ridicule
93	make up one’s mind	decide, determine
94	matter of concern	something to worry about
95	miss the boat	it’s too late
96	muffle up	to cover
97	not playing with a full deck	someone who lacks intelligence
98	note of hand	promissory note
99	null and void	invalid
100	on cloud nine	to be extremely happy
101	once and for all	completely and finally
102	once in a blue moon	vary rarely
103	one thing leads to another	series of events in which each event was caused by the previous one.
104	out of place	unsuitable
105	pink of health	extremely healthy, in perfect condition
106	play an important role	to have a significant position
107	pull yourself together	calm down
108	put on airs	behave in an unnatural way to impress others
109	shadow of one’s self	not having the strength, former self influence, etc., that one once had
110	side by side	along with
111	speak volumes	to express something very clearly and completely
112	spill the beans	give away a secret
113	take to one’s heels	to run away
114	taken a very hard line	not giving in
115	the ball is in your court	it’s your decision
116	the burning question	a crucial issue
117	the whys and wherefores	the reasons for something
118	thick and fast	in large numbers
119	tit for tat	revenge
120	told him flat	expressed opinion directly
121	tread on	walk with difficulty
122	trial and error	to try many times to succeed
123	tricks of the trade	the expertise of doing business
124	well-balanced	well adjusted
125	whole nine yards	everything, all of it
126	wouldn’t be caught dead	would never like to do something
127	with a bang	in a very exciting way

Exercises
(i) Choose the correct option to complete the given idioms.
1. A bolt from _________.
(a) the white (b) the sky (c) the green (d) the blue
Answer:
(d) the blue

2. A storm _________.
(a) at sea (b) in the ocean (c) in a coffee cup (d) in a tea cup
Answer:
(d) in a tea cup

3. Can’t judge a book, _________.
(a) by the colour (b) by its cover (c) by its pages (d) by its author
Answer:
(db) by its cover

4. Every cloud _________.
(a) is dark (b) hides the sun (c) has a silver lining (d) brings rain
Answer:
(c) has a silver lining

5. Casts an arm _________.
(a) and a face (b) and a finger (c) and a leg (d) and some money
Answer:
(c) and a leg

6. Add insult to _________.
(a) friend (b) enemy (c) neighbor (d) injury
Answer:
(d) injury

7. A penny for _________.
(a) a picture (b) honesty (c) hard work (d) your thoughts
Answer:
(d) your thoughts

8. Fortune favors
(a) the hardworking (b) the poor (c) the rich (d) the bold
Answer:
(d) the bold

9. Hit the nail _________.
(a) on the wall (b) on the door (c) in the bench (d) on the head
Answer:
(d) on the head

10. Once in a _________.
(a) blue moon (b) in a tea cup (c) new moon (d) full moon
Answer:
(a) blue moon

(ii) Give a suitable idiom for the given meanings.

1. Say something exactly right.
Answer:
To hit the nail on the head.

2. All social groups.
Answer:
All walks of life.

3. It’s raining hard.
Answer:
Its raining cats and dogs.

4. Passed away.
Answer:
Kicked the bucket.

5. Live within means.
Answer:
To make both ends meet.

6. Invalid.
Answer:
Null and void.

7. Extremely healthy.
Answer:
Pink of health.

8. Give away a secret.
Answer:
To let the cat out of the bag.

9. Revenge.
Answer:
Tit for that.

10. In trouble.
Answer:
In deep waters.

Students can Download Maths Chapter 2 Algebra Ex 2.4 Questions and Answers, Notes Pdf, Samacheer Kalvi 8th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 2 Algebra Ex 2.4

Question 1.
Fill in the blanks:

Question (i)
y = px where p ∈ Z always passes through the ………
Answer:
Origin (0, 0)
Hint:
[When we substitute x = 0 in equation, y also becomes zero. (0,0) is a solution]

Question (ii)
The intersecting point of the line x = 4 and y = – 4 is ………
Answer:
4, -4
Hint:
x = 4 is a line parallel to the y – axis and
y = – 4 is a line parallel to the x – axis. The point of intersection is a point that lies on both lines & which should satisfy both the equations. Therefore, that point is (4, -4)

Question (iii)
Scale for the given graph, on the x – axis 1 cm = ……… units y – axis 1 cm = ………. units

Answer:
3 units, 25 units
Hint:
With reference to given graph,
On the x – axis, 1cm = 3 units
y axis, 1cm = 25 units

Question 2.
Say True or False:

Question (i)
The points (1, 1) (2, 2) (3, 3) lie on a straight line.
Answer:
True
Hint:
The points (1, 1), (2, 2), (3, 3) all satisfy the equation y = x
which is straight line. Hence, it is true

Question (ii)
y = – 9x not passes through the origin.
Answer:
False
Hint:
y = – 9x substituting forx as zero, we get y = – 9 x 0 = 0
∴ for x = 0, y = 0. Which means line passes through (0, 0), hence statement is false.

Question 3.
Will a line pass through (2, 2) if it intersects the axes at (2, 0) and (0, 2).
Solution:
Given a line intersects the axis at (2, 0) & (0, 2)
Let line intercept form be expressed as
ax + by = 1 Where a & b are the x & y intercept respectively.
Since the intercept points are (2, 0) & (0, 2)
a = 2, b = 2
∴ 2x + 2y = 1
When the point (2, 2) is considered & substituted in the equation
2x + 2y = 1 we get
2 x 2 + 2 x 2 = 4 ≠ 1
∴ The point (2, 2) does not satisfy the equation. Therefore the line does not pass through (2, 2)
Alternatively graphical method:
as we can see the line doesn’t pass through (2, 2)

Question 4.
A line passing through (4, – 2) and intersects the Y – axis at (0, 2). Find a point on the line in the second quadrant.
Solution:

Line passes through (4, – 2)
y – axis intercept point – (0, 2)
using 2 point formula,
\(\frac { y-y_{ 1 } }{ x-x_{ 1 } } \) = \(\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } } \)
\(\frac{y-2}{x-0}\) = \(\frac{1-2-2}{4-0}\)
∴ \(\frac{y-2}{x}\) = \(\frac{-4}{4}\) = – 1
y – 2 = – 1 × x

∴ x + y = 2 is the equation of the line.
Any point in II quadrant will have x as negative & y as positive.
So let us take x value as – 2
∴ – 2 + y = 2
y = 2 + 2 = 4
∴ Point in II Quadrant is (-2, 4)

Question 5.
If the points P (5, 3) Q(- 3, 3) R (- 3, – 4) and S form a rectangle then find the coordinate of S.
Solution:
Plotting the points on a graph (approximately)

Steps:

1. Plot P, Q, R approximately on a graph.
2. As it is a rectangle, RS should be parallel to PQ & QR should be parallel to PS
3. S should lie on the straight line from R parallel to x – axis & straight line from P parallel to y – axis
4. Therefore, we get S to be (5, -4)

[Note: We don’t need graph sheet for approximate plotting. This is just for graphical understanding]

Question 6.
A line passes through (6, 0) and (0, 6) and an another line passes through (- 3, 0) and (0, – 3). What are the points to be joined to get a trapezium?
Solution:
In a trapezium, there are 2 opposite sides that are parallel. The other opposite sides are non-parallel.
Now, let us approximately plot the points for our understanding [no need of graph sheet]

1. Plot the points (0, 6), (6, 0), (-3, 0) & (0, – 3)
2. Join (0, 6) & (6, 0)
3. Join (-3, 0) & (0, -3)
4. We find that the lines formed by joining the points are parallel lines.
5. So, for forming a trapezium, we should join (0, 6), (-3, 0) & (0, -3), (6, 0)

Question 7.
Find the point of intersection of the line joining points (- 3, 7) (2, – 4) and (4, 6) (- 5, 7). Also find the point of intersection of these lines and also their intersection with the axis.
Solution:

Equation of line joining 2 points by 2 point formula is given by
\(\frac { y-y_{ 1 } }{ x-x_{ 1 } } \) = \(\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } } \)
∴ \(\frac{y-7}{x-(-3)}\) = \(\frac{-4-7}{2-(-3)}\)
\(\frac{y-7}{x+3}\) = \(\frac{-11}{2+3}\)
∴ \(\frac{y-7}{x+3}\) = \(\frac{-11}{5}\)
Cross multiplying, we get

Transposing the variables, we get
11x + 5y = 35 – 33 = 2
11x + 5y = 2 – Line 1
Similarly, we should find out equation of second line

∴ 9y – 54 = 13x – 52
9y – 13x = 2 – Line 2
For finding point of intersection, we need to solve the 2 line equation to find a point that will satisfy both the line equations.
∴ Solving for x & y from line 1 & line 2 as below
11x + 5y = 2 ⇒ multiply both sides by 13,
11 x 13x + 5 x 13y = 26
Line 2:
9y – 13x = 2 ⇒ multiply both sides by 11
9 x 11y – 13 x 11x = 22

Substituting this value of y in line 1 we get
11x + 5y = 2
11x + 5 x \(\frac{12}{41}\) = 2
11x = 2 – \(\frac{60}{41}\) = \(\frac{82-60}{41}\) = \(\frac{22}{41}\)
x = \(\frac{2}{41}\)
∴ Point of intersection is (\(\frac{2}{41}\) \(\frac{12}{41}\))
To find point of intersection of the lines with the axis, we should substitute values & check
Line 1:
11x + 5y = 2
Point of intersection of line with x – axis, i.e y coordinate is ‘0’
∴ put y = 0 in above equation
∴ 11x – 5 x 0 = 2
11x + 0 = 2
x = \(\frac{2}{11}\)
∴ Point is (\(\frac{2}{11}\), 0)
Similarly, point of intersection of line with y – axis is when x – coordinate becomes ‘0’
∴ put x = 0 in above equation
∴ 11 x 0 + 5y = 2
∴ 0 + 5y = 2
y = \(\frac{2}{5}\)
∴ Point is (0, \(\frac{2}{5}\))
Similarly for line 2,
9y – 13x = 2
For finding x intercept, i.e point where line meets x axis, we know thaty coordinate becomes ‘0’
∴ Substituting y – 0 in above eqn. we get
9 x 0 – 13x = 2
∴ 0 – 13x = 2
x = \(\frac{-2}{13}\)
∴ Point is (\(\frac{-2}{13}\), 0)
Similarly for y – intercept, x – coordinate becomes ‘0’,
∴ Substituting for x = 0 in above equation, we get
9y – 13 x 0 = 2
9y – 0 = 2
9y = 2
y = \(\frac{2}{9}\)
Point is (0, \(\frac{2}{9}\))

Question 8.
Draw the graph of the following equations:

1. x = – 7
2. y = 6

Solution:

Question 9.
Draw the graph of

1. y = – 3x
2. y = x – 4

Solution:
To draw graph, we need to find out some points.
1. for y = – 3x, let us first substituting values & check
put x = 0
y = – 3 x 0 = 0 ∴ (0,0) is a point
put x = 1
y = – 3 x 1 = – 3 ∴ (1, – 3) is a point
If join these 2 points, we will get the line

2. for y = x – 4
put x = 0
y = 0 – 4 = -4 ∴ (0, – 4) is a point
x = 4
y = 4 – 4 = 0 ∴ (4, 0) is a point
Now let us plot the points & join them on graph

Question 10.
Find the values

Solution:
Let y = x + 3
(i) if x = 0
y = 0 + 3 = 3
∴ y = 3

(ii) y = 0
0 = x + 3
∴ x = – 3

(iii) x = – 2
y = – 2 + 3
∴ y = 1

(iv) y = -3
-3 = x + 3
∴ x = -6

Let 2x + 7 – 6 = 0
(i) x = 0
2 x 0 + y – 6 = 0
∴ 7 = 6

(ii) y = 0
2x + 0 – 6 = 0
2x = 6
x = 3

(iii) x = – 2
2 x (- 2) + y – 6 = 0
y – 10 = 0
y = 10

(iv) y = -3
2x – 3 – 6 = 0
2x = 9
x = \(\frac{9}{2}\)

Question 11.
The following is a table of , values connecting the radii of a few circles and their circumferences (Taking π = \(\frac{22}{7}\)) Illustrate the relation with a graph and find

1. The radius when the circumference is 242 units.
2. The circumference when the radius is 24.5 units.

Solution:

r = 24.5 Circumference?

Steps :

1. Draw the axis, x – axis = radius & y – axis = circumference
2. Mark the points by choosing scale of 1 cm = 7 units for x axis & 1 cm = 44 units for y – axis
3. Join the points to form a line.
4. Now for r value = 24.5 (mid value between 21 & 28), draw vertical line to touch the main line & from there drop line parallel to x axis and note where it meets y axis.

It meets between 132 & 176. Taking the mid value
i.e \(\frac{132+176}{2}\) = 154, we get circumference of 154 when r = 24.5.
Similarly, for circumference of 242, we get r value to be 38.5

Question 12.
An over-head tank is full with water. Water leaks out from it, at a constant rate of 10 litres per hour. Draw a “time-wastage” graph for this situation and find

1. The water wasted in 150 minutes
2. The time at which 75 litres of water is wasted.

Solution:
From over head tank, water leaks out at 10 l/hr.
∴ Let us see how much leakage happens with time
Time     Leakage
1 hr        10 ltrs.
2 hrs       20 ltrs.
3 hrs       30 ltrs.
4 hrs       40 ltrs.. and so on
150 min = 120 min + 30 min
= 2 hr 30 min = 2 \(\frac{1}{2}\) hrs
Now let us plot a graph between time & water leakage

Water wasted in 150 min (2\(\frac{1}{2}\) hrs) = 25 litres
Time at which 75 litre of water is wasted = 7\(\frac{1}{2}\) hrs = 450 minutes.

Students can Download Maths Chapter 5 Information Processing Ex 5.1 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.1

Question 1.
Match the given patterns of shapes with the appropriate number pattern and its generalization.


Solution:
(i) (d)
(ii) (a)
(iii) (c)
(iv) (c)
(v) (b)

Objective Type Questions

Question 2.
Identify the correct relationship between x andy from the given table.

(i) y = 4x
(ii) y = x + 4
(iii) y = 4
(iv) y = 4 × 4
Answer:
(i) y = 4x

Question 3.
Identify the correct relationship between x and y from the given table.

(i) y = -2x
(ii) y = +2x
(iii) y = +3x
(iv) y = -3x
Answer:
(iv) y = -3x

Students can Download Maths Chapter 4 Geometry Ex 4.2 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 4 Geometry Ex 4.2

Question 1.
Given that ∆ABC = ∆DEF (i) List all the corresponding congruent sides
(ii) List all the corresponding congruent angles.
Solution:
Given ∆ABC ≅ DEF.

(i) Corresponding congruent sides.
\(\overline{A B}\) = \(\overline{D E}\); \(\overline{B C}\) = \(\overline{E F}\); \(\overline{A C}\) = \(\overline{D F}\)

(ii) Corresponding congruent angles.
∠ABC = ∠DEF; ∠BCA = ∠EFD ; ∠CAB = ∠FDE

Question 2.
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles.
(i)
(ii)
Solution:
Given ∆PQR ≅ ∆LNM
(i) (a) Corresponding sides
\(\overline{P Q}\) = \(\overline{L N}\) ; \(\overline{P Q}\) = \(\overline{L M}\) ; \(\overline{R Q}\) = \(\overline{M N}\)
(b) Corresponding angles
∠RPQ = ∠NLM; ∠PQR = ∠LNM; ∠PRQ = ∠LMN

(ii) Given ∆PQR ≅ ∆NML
(a) Corresponding angles
\(\overline{Q R}\) = \(\overline{L M}\) ; \(\overline{R P}\) = \(\overline{L N}\); \(\overline{P Q}\) = \(\overline{M N}\)
(b) Corresponding angles
∠PQP = ∠NMN; ∠QRP = ∠MLN; ∠RPQ = ∠LNM

Question 3.
Find the unit digit of expanded form.

(i) ∠A and ∠G
(ii) ∠B and ∠E
(iii) ∠B and ∠G
(iv) \(\overline{A C}\) and \(\overline{G F}\)
(v) \(\overline{B A}\) and \(\overline{F G}\)
(vi) \(\overline{E F}\) and \(\overline{B C}\)
Solution:
Given ∆ABC ≅ ∆EFG. Also from given triangles.
\(\overline{A B}\) = \(\overline{F G}\) \(\overline{B C}\) = \(\overline{G F}\) \(\overline{A C}\) = \(\overline{E F}\)
Also ∠A = ∠F ∠B = ∠G ∠C = ∠E
Answer:
(i) ∠A and ∠G are not corresponding angles.
(ii) ∠B and ∠E are not corresponding angles.
(iii) ∠B and ∠G are corresponding angles.
(iv) \(\overline{A C}\) and \(\overline{G F}\) are not corresponding sides.
(v) \(\overline{B A}\) and \(\overline{F G}\) are corresponding sides.
(vi) \(\overline{E F}\) and \(\overline{B C}\) are not corresponding sides.

Question 4.
State whether the two triangles are congruent or not. Justify your answer.

Solution:
(i) Let the given triangle be ∆ABC. \(\overline{A D}\) divides ∆ABC into two parts giving ∆ABD and ∆ACD.
In ∆ABD and ∆ACD

\(\overline{A B}\) = \(\overline{A C}\) (given)
\(\overline{B D}\) = \(\overline{A D}\) (common side)
∠BAD = ∠CAD (included angles)
∴ By SAS criterion ∆ABD ≅ ∆ACD.

(ii) Let the given triangles in the figure be ∆ABC and ∆DCB.
In both the triangles

\(\overline{B C}\) = \(\overline{B C}\) (Common side)
\(\overline{A B}\) = \(\overline{D C}\)
\(\overline{A C}\) = \(\overline{B D}\)
∴ By SSS Criterion ∆ABC ≅ ∆DCB

(iii) Let the given triangles be ∆ABC and ∆CDE.

Here \(\overline{A C}\) = \(\overline{C E}\) (given)
∠BAC = ∠DEC (given)
∠ACB = ∠DCE (vertically opposite angles)
Two angles and the included side are equal.
Therefore by ASA criterion ∆ABC ≅ ∆CDE.

(iv) Let the two triangles be ∆XYZ and ∆XYW

Here ∠W = ∠Z = 90°
\(\overline{X Y}\) = \(\overline{X Y}\) (Common Hypothenure)
\(\overline{X W}\) = \(\overline{X Z}\) (given)
By RHS criterion ∆XYZ ≅ ∆XYW

(v) Let the two triangles be ∆ABC and ∆ADC

In both the triangles \(\overline{A C}\) = \(\overline{A C}\) (common sides)
\(\overline{A D}\) = \(\overline{B C}\) (given)
\(\overline{A B}\) = \(\overline{D C}\) (given)
By SSS criterion ∆ABC ≅ ∆ADC.

Question 5.
To conclude the congruency of triangles, mark the required information in the following figures with reference to the given congruency criterion.

Solution:
(i) In the given triangles one angle is equal and a side is common and so equal.

To satisfy ASA criterion one more angle should be equal such that the common side is the included side of both angles of a triangle.
The figure will be as follows.

(ii) In the two given triangles two sides of one triangle is equal to two sides of the other triangle.

To satisfy SSS criterion the third sides mut be equal.

(iii) The given triangles have one side in common. They are right angled tringles.

To satisfy RHS criterion their hypotenuse must be equal.

(iv) In the given triangles two angles of one triangle is equal to two angles of the other triangles?

To satisfy ASA criterion included side of two angles must be equal.

(v) In both the triangles one of their sides are equal.

One of their angles are equal or they are vertically opposite angles.
To satisfy SAS criterion, one more side is to be equal such that the angle is the included of the equal sides.

Question 6.
For each pair of triangles state the criterion that can be used to determine the congruency?

Solution:
(i) Given two pair of sides are equal and one side is common to both the triangles.
∴ SSS congruency criterion is used.

(ii) One of the sides and one of the angles are equal.
∴ One more angle is vertically opposite angle and so it is also equal.
ASA criterion is used.

(iii) From the figure hypotenuse and one side are equal in both the triangles.
RHS congruency criterion is used. (∵ Considering ∆ABC and ∆BAD)
∠A = ∠B = 90°
AD = BC
AB = AB (common)
∴ AC = BD (hypotenuse)

(iv) By ASA criterion both triangles are congruent.

(v) By ASA criterion both triangles are congruent. Since two angles in one triangle are equal to two corresponding angles of the other triangle. Again one side is common to both triangle and the side is the included side of the angles.

(vi) Two sides are equal. One angle is vertically opposite angles and one equal.
By SAS criterion both triangles are cogruent.

Question 7.
I. Construct a triangle XYZ with the given conditions.

(i) XY = 6.4 cm, ZY = 7.7 cm and XZ = 5 cm
Solution:


Construction:
Step 1: Draw a line. Marked Y and Z on the line such that YZ 7.7 cm.
Step 2: With Y as centre drawn an arc of radius 6.4 cm above the line YZ.
Step 3: With Z as centre, drwan an arc or radius 5 cm to intersect arc drawn in steps. Marked the point of intersection as X.
Step 3: Joined YX and ZX. Now XYZ is the required triangle.

(ii) An equilateral triangle of side 7.5 cm
Solution:

Construction:
Step 1: Drawn a line. Marked X and Y on the line such that XY = 7.5 cm.
Step 2: With X as centre, drawn an arc of radius 7,5 cm above the line XY.
Step 3: With Y as centre, drawn an arc of radius 7.5 cm to intersect arc drawn in steps. Marked the point of intersection as Z.
Step 4: Joined XZ and YZ. Now XYZ in the required triangle.

(iii) An isosceles triangle with equal sides 4.6 cm and third side 6.5 cm
Solution:

Construction: .
Step 1: Drawn a line. Marked X and Y on the line such that XY = 6.5 cm.
Step 2: With X as centre, drawn an arc of radius 4.6 cm above the line XY
Step 3: with Y as centre, drawn an arc of radius 4.6 cm to intersect arc drawn in steps. Marked the point of intersection as Z.
Step 4: Joined XZ and YZ. Now XYZ is the required triangle.

II. Construct a triangle ABC with given conditions.

(i) AB = 7 cm, AC = 6.5 cm and ∠A = 120°.
Solution:

Construction:
Step 1: Drawn a line. Marked A and B on the line such that AB = 7 cm.
Step 2: At A, drawn a ray AX making an angle of 120° with AB.
Step 3: With A as centre, drawn an arc of radius 6.5 cm to cut the ray AX. Marked the point of intersection as C.
Step 4: Joined BC.
ABC is the required triangle.

(ii) BC = 8 cm, AC = 6 cm and ∠C = 40°.
Solution:


Construction:
Step 1: Drawn a line. Marked B and C on the line such fhat BC = 8 Cm.
Step 2: At C, drawn a ray CY making an angle of 40° with BC.

Step 3: With C as centre, drawn an arc of radius 6 cm to cut the ray CY, marked the point of intersection as A.
Step 4: Joined AB.
AB is the required triangle.

(iii) An isosceles obtuse triangle with equal sides 5 cm
Solution:

Construction:
Step 1: Drawn a line. Marked B and C on the line such that BC = 5 cm.
Step 2: At B drawn a ray BY making on obtuse angle 110° with BC.
Step 3: With B as centre, drawn an arc of radius 5 cm to cut ray BY. Marked the point of intersection as C.
Step 4: Joined BC. ABC is the required triangle.

III. Construct a triangle PQR with given conditions.

(i) ∠P = 60°, ∠R = 35° and PR = 7.8 cm
Solution:

Construction:
Step 1: Drawn a line. Marked P and R on the line such that PR = 7.8 cm.
Step 2: At P, drawn a ray PX making an angle of 60° with PR.
Step 3: At R, drawn another ray RY making an angle of 35° with PR. Mark the point of intersection of the rays PX and RY as Q.
PQR is the required triangle.

(ii) ∠P = 115°, ∠Q = 40° and PQ = 6 cm
Solution:

Construction:
Step 1: Drawn a line. Marked P and Q on the line such that PQ = 6 cm.
Step 2: At P, drawn O ray PX making an angle of 115° with PQ.
Step 3: At Q, drawn another ray QY making an angle of 40° with PQ. Marked the point of intersection of the rays PX and Q Y as R.
PQR is the required triangle.

(iii) ∠Q = 90°, ∠R = 42° and QR = 5.5 cm
Solution:

Construction:
Step 1: Drawn a line. Marked Q and R on the line such that QR = 5.5 cm.
Step 2: At Q, drawn a ray QX making an angle of 90° with QR.
Step 3: At R, drawn another ray RY making an angle of 42° QR. Marked the point of intersection of the rays QX and RY as P.
PQR is the required triangle.

Objective Type Questions

Question 8.
If two plans figures are congruent then they have
(i) same size
(ii) same shape
(iii) same angle
(iv) same shape and same size
Answer:
(iv) same shape and same size

Question 9.
Which of the following methods are used to check the congruence of plane figures?
(i) translation method
(ii) superposition method
(iii) substitution method
(iv) transposition method
Answer:
(ii) superposition method

Question 10.
Which of the following rule is not sufficient to verify the congruency of two triangles.
(i) SSS rule
(ii) SAS rule
(iii) SSA rule
(iv) ASA rule
Answer:
(iii) SSA rule

Question 11.
Two students drew a line segment each. What is the condition for them to be congruent?
(i) They should be drawn with a scale.
(ii) They should be drawn on the same sheet of paper.
(iii) They should have different lengths.
(iv) They should have the same length.
Answer:
(iv) They should have the same length.

Question 12.
In the given figure, AD = CD and AB = CB. Identify the other three pairs that are equal.

(i) ∠ADB = ∠CDB, ∠ABD = ∠CBD, BD = BD
(ii) AD = AB, DC = CB, BD = BD
(iii) AB = CD, AD = BC, BD = BD
(iv) ∠ADB = ∠CDB, ∠ABD = ∠CBD, ∠DAB = ∠DBC
Answer:
(i) ∠ADB = ∠CDB, ∠ABD = ∠CBD, BD = BD

Question 13.
In ∆ABC and ∆PQR, ∠A = 50° = ∠P, PQ = AB, and PR = AC. By which property ∆ABC and ∆PQR are congruent?
(i) SSS property
(ii) SAS property
(iii) ASA property
(iv) RHS property
Answer:
(ii) SAS property

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Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 2 Algebra Ex 2.5

Miscellaneous Practice Problems

Question 1.
The sum of three numbers is 58. The second numberis three times of two-fifth of the first number and the third number is 6 less than the first number. Find the three numbers.
Solution:
Here what we know
a + b + c = 58 (sum of three numbers is 58)
Let the first number be ‘x’
b = a + 3 (the second number is three times of \(\frac{1}{2}\) of the first number)
b = 3 x \(\frac{2}{5}\)x = \(\frac{6}{5}\)x
Third number = x – 6
Sum of the numbers is given as 58.
∴ x + \(\frac{6}{5}\)x + (x – 6) = 58
Multiplying by 5 throughout, we get
5 × x + 6x + 5 × (x – 6) = 58 x 5
5x + 6x + 5x – 30 = 290
∴ 16x = 290 + 30
∴ 16x = 320
∴ x = \(\frac{320}{16}\)x = 20
Answer:
1st number =20
2nd number = 3 x \(\frac{2}{5}\) x 20 = 24
3rd number = 24 – 6 = 14

Question 2.
In triangle ABC, the measure of ∠B is two third the measure of ∠A. The measure of ∠C is 20° more than the measure of ∠A. Find the measures of the three angles.
Solution:
Let angle ∠A be a°
Given that ∠B = \(\frac{2}{3}\) x ∠A = \(\frac{2}{3}\)a
& given ∠C = ∠A + 20 = a + 20
Since A, B & C are angles of a triangle, they add up to 180° (∆ property)
∠A + ∠B + ∠C = 180°
a + \(\frac{2}{3}\) a + a + 20 = 180°
\(\frac{3a+2a+3a}{3}\) + 20 = 180°
\(\frac{8a}{3}\) = 180 – 20 = 160°

∠C = 80°

Question 3.
Two equal sides of an isosceles triangle are 5y – 2 and 4y + 9 units. The third side is 2y + 5 units. Find y and the perimeter of the triangle.
Solution:
Given that 5y – 2 & 4y + 9 are the equal sides of an isosceles triangle.
The 2 sides are equal

∴ 5y – 4y = 9 + 2 (by transposing)
∴ y = 11
∴ 1st side = 5y – 2 = 5 x 11-2 = 55 – 2 = 53
2nd side = 53
3rd side = 2y + 5 = 2 x 11 + 5 = 22 + 5 = 27
Perimeter is the sum of all 3 sides
∴ P = 53 + 53 + 27 = 133 units

Question 4.
In the given figure, angle XOZ and angle ZOY form a linear pair. Find the value of x.

Solution:
Since ∠XOZ & ∠ZOY form a linear pair,
by property, we have their sum to be 180°
∴ ∠XOZ + ∠ZOY = 180°
3x – 2 + 5x + 6 = 180°
8x + 4 = 180 = 8x = 180 – 4
∴ 8x = 176 ⇒ x = \(\frac{176}{8}\) ⇒ x = 22°
XOZ = 3x – 2 = 3 x 22 – 2 = 66 – 2 = 64°
YOZ = 5x + 6 = 5 x 22 + 6
= 110 + 6 = 116

Question 5.
Draw a graph for the following data:

Does the graph represent a linear relation?
Solution:
Graph between side of square & area

When we plot the graph, we observe that it is not a linear relation.

Challenging Problems

Question 6.
Three consecutive integers, when taken in increasing order and multiplied by 2, 3 and 4 respectively, total up to 74. Find the three numbers.
Solution:
Let the 3 consecutive integers be ‘x’, ’x + 1 & ‘x + 2’
Given that when multiplied by 2, 3 & 4 respectively & added up, we get 74

Simplifying the equation, we get
2x + 3x + 3 + 4x + 8 = 74
9x + 11 = 74
9x = 63 ⇒ x = \(\frac{63}{9}\) = 7
First number = 7
Second numbers = x + 1
Third numbers = x + 2
∴ The numbers are 7, 8 & 9

Question 7.
331 students went on a field trip. Six buses were filled to capacity and 7 students had to travel in a van. How many students were there in each bus?
Solution:
Let the number of students in each bus be ‘x’
number of students in 6 buses = 6 × x = 6x
Apart from 6 buses, 7 students went in van
A total number of students is 331
∴ 6x + 7 = 331
∴ 6x = 331 – 7 = 324
∴ x = \(\frac{324}{6}\) = 54
∴ There are 54 students in each bus.

Question 8.
A mobile vendor has 22 items, some which are pencils and others are ball pens. On a particular day, he is able to sell the pencils and ball pens. Pencils are sold for ₹ 15 each and ball pens are sold at ₹ 20 each. If the total sale amount with the vendor is ₹ 380, how many pencils did he sell?
Solution:
Let vendor have ‘p’ number of pencils & ‘b’ number of ball pens
Given that total number of items is 22
∴ p + b = 22
Pencils are sold for ₹ 15 each & ball pens for ₹ 20 each
total sale amount = 15 x p + 20 x b
= 15p + 20b which is given to be 380.
∴ 15p + 20b = 380
Dividing by 5 throughout,
\(\frac{15p}{5}\) + \(\frac{20b}{5}\) = \(\frac{380}{5}\)
⇒ 3p + 4b = 76
Multiplying equation (1) by 3 we get
3 x 7 + 3 x b = 22 x 3
⇒ 3p + 3b = 66
Equation (2) – (3) gives

∴ b = 10
∴ p = 12
He sold 12 pencils

Question 9.
Draw the graph of the lines y = x, y = 2x, y = 3x and y = 5x on the same graph sheet. Is there anything special that you find in these graphs?
Solution:

1. y = x
2. y = 2x
3. y = 3x
4. y = 5x

1. y = x
When x = 1, y = 1
x = 2, y = 2
x = 3, y = 2

2. y = 2x
When x = 1, y = 2
X = 2, y = 4
X = 3, y = 6

3. y = 3x
when x = 1, y = 3
x = 2, y = 6
x = 3, y = 9

4. y = 5x
When x = 1, y = 5
x = 2, y = 10
x = 3, y = 15

When we plot the alijpve points & join the points to form line, we notice that the lines become progressively steeper. In other words, the slope keeps increasing.

Question 10.
Consider the number of angles of a convex polygon and the number of sides of that polygon. Tabulate as follows:

Use this draw a graph illustrating the relations hip between the number of angles and the number of sides of a polygon.
Solution:
Angles:

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Tamilnadu Samacheer Kalvi 9th English Grammar Active Voice, Passive Voice

Read the following sentences and analyze the difference.
The team leader presented the report.
The report was presented by the team leader.

1. In the first sentence, the verb shows that the subject is the doer of the action. Therefore, the sentence is in active voice.
2. In the second sentence, the verb shows that the subject is not the doer of the action. Therefore, the sentence is in passive voice.

We use the Passive voice when –

• the focus is on the action rather than the doer of the action.
  (e.g.), About 50 percent of the graduates are employed in IT-related sectors.
• we do not know who the doer is.
  (e.g.) My bike was stolen yesterday.
• we talk of a system or a process.
  (e.g.) The vegetables are washed well. Then, they are cut into cubes.
• we write newspaper headlines and notices at public places, (‘be’ verb is omitted as the language has to be concise)
  (e.g.) 20 sportsmen felicitated by PM.
• we describe changes that have taken place.
  (e.g.) Our school looks completely different. The whole place has been painted.

Look at the table below. It shows the changes in tense while changing sentences from active voice in to passive voice.

Tense	Active Voice	Passive Voice
Simple Present	He makes coffee.	Coffee is made by him.
Present Continuous	He is making coffee.	Coffee is being made by him.
Present Perfect	He has made coffee.	Coffee has been made by him.
Simple Past	He made coffee.	Coffee was made by him.
Past Continuous	He was making coffee.	Coffee was being made by him.
Past Perfect	He had made coffee.	Coffee had been made by him.
Simple Future	He will make coffee.	Coffee will be made by him.
Future Perfect	He will have made coffee.	Coffee will have been made by him.

When using the active voice, the subjects are the ones performing the action.
God loves all men.
Birds build nests.
Dogs eats bones.

In these three sentences the subject does the action. Hence they are in the active voice. In the active voice, the verb takes an object.
All men are loved by God.
Nests are built by birds.
Bones are eaten by dogs.

Rules for changing Active Voice into Passive Voice:

• Identify the subject, the verb and the object: SVO.
• Change the object into subject.
• Put the suitable helping verb or auxiliary verb according to the tense given.
• Change the verb into past participle of the verb.
• Add the preposition “by”
• Change the subject into object.

Active Voice	Passive Voice
Columbus discovered America.	America was discovered by Columbus.
Who did this work?	By whom was this work done?
Open the window.	Let the window be opened.
He is writing a letter.	A letter is being written by him.
I will finish the work.	The work will be finished by me.
Somebody cleaned the room yesterday.	The room was cleaned yesterday.

How to form passive forms of verbs?

Tense	Active	Passive
Present Tense	do, does	is done (Singular) are done (Plural)
Past Tense	did	was done (Singular) were done (Plural)
Future Tense	will / can / may / must → do	will / can etc. → be done
Present Continuous Tense	am doing is doing	is being done (Singular) are being done (Plural)
Past Continuous Tense	are doing was doing	was being done (Singular) were being done (Plural)
Future Continuous Tense	will be doing shall be doing	No Passive Voice
Present Perfect Tense	have done has done	have been done (Plural) has been done (Singular)
Past Perfect Tense	had done	had been done
Future Perfect Tense	shall have done will have done	will have been done
Present Perfect Continuous Tense	has been doing have been doing	No Passive Voice
Past Perfect Continuous Tense	had been doing	No Passive Voice
Future Perfect Continuous Tense	shall have been doing will have been doing	No Passive Voice

Changes of Pronouns:

Active Voice	Passive Voice
I	me
we	us
you	you
he	him
she	her
it	it
they	them

Type 1: Statements:

Active Voice	Passive Voice
I write a letter	A letter is written by me
We must keep the rule	The rule must be kept by us
You bought a book	A book was bought by you
He closed the window	The window was closed by him
She was writing letters	Letters were being written by her
I had posted a letter	A letter had been posted by me
I do not drink tea	Tea is not drunk by me
She does not eat a mango	A mango is not eaten by her
1 Ie will have finished his work	The work will have been finished by him
They are digging a well	A well is being dug by them

Type 2: Imperative Sentence :
If the given sentence in the active voice is in the imperative, to get the passive voice use ‘Let’.
Passive Voice = Let + Object + be + Past Participle

Active Voice	Passive Voice
Help me	You are requested to help me.
Sing a song	Let a song be sung
Open the door	Let the door be opened
Don’t eat this fruit	You are warned not to eat this fruit.

• We can begin the passive sentence with ‘you’ if we want to put emphasis on the person addressed to.

Type 3 : Interrogative Questions in the Passive :
If the question in the Active Voice begins with a Helping verb, the Passive voice must also begin with a suitable helping verb. Supposing the question begins with ‘Wh or How’ form (what, when, how …) the Passive Voice must begin with the same.

Active Voice	Passive Voice
Are you writing a letter?	Is a letter being written by you?
Is she beating the child?	Is the child being beaten by her?
Will you accept the position?	Will the position be accepted by you?
Who broke the window?	By whom was the window broken?
Why did you write such a letter?	Why was such a letter written by you?
Where can you hide this box?	Where can this box be hidden by you?

If a sentence contains two objects namely Indirect Object and Direct Object in the Active Voice, two forms of Passive Voice can be formed.

• She brought me a cup of coffee. (AV)
  I was brought a cup of coffee by her. (PV) (or)
  A cup of coffee was brought to me by her. (PV)
• The teacher teaches us grammar. (AV)
  We are taught grammar by the teacher. (PV) (or)
  Grammar is taught [to] us by the teacher. (PV)

Infinitive and Gerund :

• I want to shoot the tiger. (AV)
  I want the tiger to be shot. (PV)
• I remember my father taking me to the theatre. (AV)
  I remember being taken to the theatre by my father. (PV)

Passive to Active form:
While changing Passive Voice into Active Voice, we must keep in mind all the rules of the Active Voice in the reverse order. We come across sentences in the Passive Voice without subject or agent. In this case, supply the appropriate subject.

Changing Passive Voice to Active Voice.

Passive Voice	Active Voice
The thief was finally arrested.	The police finally arrested the thief.
We were taught grammar.	The teacher taught us grammar.
My purse has been stolen.	Somebody has stolen my purse.
The patients have looked after.	The doctor looked after the patients.

• Last year, the Swach Bharat scheme was announced by the Government.
• Rare plants are found in Silent Valley.

In the first sentence, the doer/agent is explicitly mentioned because the doer is important in that sentence. But in the second sentence, it is not so, because either the agent or doer of the action is too obvious or unknown.

The passive construction is quite common in scientific/technical/ business writing. In these types of objective writing, the emphasis is usually on the action or process or thing that is described. So the ‘by’ phrase is generally omitted in these writings. It is called Impersonal Passive.

• They say that might is right.
  It is said that might is right.
• One finds mosquitoes everywhere.
  Mosquitoes are found everywhere.
• He gave us a cheque.
  A cheque was given to us.

Exercises
(i) Choose the correct passive form for the following sentences in active voice.

1. I did not beat her.
(a) She is not beaten by me.
(b) She has not beaten by me.
(c) She was not beaten by me.
Answer:
(c) She was not beaten by me.

2. I will never forget this experience.
(a) This experience is not forgotten by me.
(b) This experience would never be forgotten by me.
(c) This experience will never be forgotten by me.
Answer:
(c) This experience will never be forgotten by me.

3. Mother made a cake yesterday.
(a) A cake made by mother yesterday.
(b) A cake is made by mother yesterday,
(c) A cake was made by mother yesterday.
Answer:
(c) A cake was made by mother yesterday.

4. The boy congratulated the girl.
(a) The girl was congratulated by the boy.
(b) The girl had congratulated by the boy.
(c) The girl congratulated the boy.
Answer:
(a) The girl was congratulated by the boy.

5. Did she do her duty?
(a) Was she done her duty?
(b) Was her duty done by her?
(c) Had her duty done by her?
Answer:
(b) Was her duty done by her?

6. The tiger was chasing the deer.
(a) The deer was chased by the tiger.
(b) The deer was being chased by the tiger,
(c) The deer had chased by the tiger.
Answer:
(b) The deer was being closed by the tiger

7. She has written a novel.
(a) A novel has written by her.
(b) A novel has been written by her.
(c) A novel had written by her.
Answer:
(b) A novel has been written by her.

8. She has learned her lessons.
(a) Her lessons has learned by her.
(b) Her lessons have been learned by her.
(c) Her lessons had been learned by her.
Answer:
(b) Her lessons have been learned by her.

9. Have you finished the report?
(a) Has the report finished by you?
(b) Has the report been finished by you?
(c) Had the report been finished by you?
Answer:
(b) Has the report been finished by you?

10. The police have caught the thief.
(a) The thief has been caught by the police.
(b) The thief was caught by the police.
(c) The thief had been caught by the police.
Answer:
(a) The thief has been caught b– police,

(ii) Rewrite the following sentences into active voice.

1. We are taught grammar by Mr. Harsha.
Answer:
Mr. Harsha teaches us grammar.

2. He was praised by the teacher.
Answer:
The teacher praised him.

3. The injured were taken to the hospital by the firemen.
Answer:
The firemen took the injured to the hospital.

4. The town was destroyed by an earthquake.
Answer:
An earthquake destroyed the town.

5. The teacher was pleased with the boy’s work.
Answer:
The boy’s work pleased the teacher.

6. The building was damaged by the fire.
Answer:
The fire damaged die building.

7. By whom were you taught Hindi?
Answer:
Who taught you Hindi? ,

8. You will be given a ticket by the manager.
Answer:
The manager will give you a ticket.

9. The streets were thronged with spectators.
Answer:
Spectators thronged the streets.

10. We will be blamed by everyone.
Answer:
Everyone will blame us.

11. The trees were blown down by the wind.
Answer:
The wind blew down the trees.

12. The thieves were caught by the police.
Answer:
The police caught the thieves.

13. The letter was posted by Alice.
Answer:
Alice posted the letter.

14. We were received by the hostess.
Answer:
The hostess received us.

15. The snake was killed with a stick.
Answer:
They / somebody killed the snake with a stick.

16. The minister was welcomed by the people.
Answer:
The people welcomed the minister.

17. He was found guilty of murder.
Answer:
They found him guilty of murder.

18. This house was built by Afsar.
Answer:
After wilting this house.

(iii) Rewrite the following sentences in the passive voice.

1. She is writing a poem.
Answer:
A poem is being written by her.

2. The team has won the series.
Answer:
The series has been won by the team.

3. Can you break the door?
Answer:
Can the door be broken by you?

4. Will she sing a song?
Answer:
Will a song be sung by her?

5. Is he speaking English?
Answer:
Is English being spoken by him?

6. Are you eating a banana?
Answer:
Is a banana being eaten by you?

7. Why are you washing the car?
Answer:
Why is the car being washed by you ?

8. When will he give the money?
Answer:
When will the money be given by him?

9. Where will he meet you?
Answer:
Where will you be met by him?

10. How do you make a cake?
Answer:
How is a cake made by you?

11. Who did you tell the story?
Answer:
To whom was the story told by you?

12. Lighting struck him.
Answer:
He was struck by lighting.

13. The language that he used quite shocked me.
Answer:
I was quite shocked by the language that he used.

14. We were both filled with horror by the sight of that event.
Answer:
The sight of the event filled both of us with horror.

15. I was much hurt by his voice and manner.
Answer:
His voice and manner hurt me much.

16. They were welcomed back by the city on their return.
Answer:
The city welcomed back them on their return.

17. He was punished by the master for speaking in the class. ‘
Answer:
The master punished him for speaking in class.

18. Many objections were raised by us to the plan that was proposed by him.
Answer:
He proposed many plans that we raised many objections.

19. Will he not be persuaded to work harder by a sense of duty?
Answer:
Will a sense of duty not persuade him to work?

20. I was called upon by the meeting to give my reasons.
Answer:
The meeting called upon me to give my reasons.

21. He was known by me by his voice when I was spoken to by him in the dark.
Answer:
I knew him by his voice when he spoke to me in the dark.

22. His return was not expected by us.
Answer:
He did not expect his return.

(iv) Complete these sentences with the verbs in brackets. Use the present simple passive.

I. E-mails _________ and received by most internet users. (send)
Answer:
are sent

2. Information about goods and services _________ (find)
Answer:
is found

3. Go&ls and services _________ in e-shops. (buy)
Answer:
are bought

4. Online newspapers and magazines _________ mostly by adult users. (read)
Answer:
are read

5. The internet _________ for social networking, especially by young people. (use)
Answer:
is used

6. relephone and video calls _________ (make)
Answer:
are made

7. Videos and films _________ (watch)
Answer:
are watched

8. Listening and music streaming activities _________ (cany out)
Answer:
are carried out

9. Hotel accommodation _________ by travellers. (search for)
Answer:
is searched for

10. Financial transactions through internet banking _________ (do)
Answer:
are done