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Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 4 Geometry Ex 4.1
Question 1.
Fill in the blanks:
(a) Every triangle has at least …….. acute angles.
(b) A triangle in which none of the sides equal is called a ………
(c) In an isosceles triangle ……… angles are equal.
(d) The sum of three angles of a triangle is ……….
(e) A right-angled triangle with two equal sides is called ………
Solution:
(a) two
(b) scalene triangle
(c) two
(d) 180°
(e) isosceles right-angled triangle
Question 2.
Match the following:
| (i) No sides are equal | Isosceles triangle |
| (ii) One right angle | Scalene triangle |
| (iii) One obtuse angle | Right-angled triangle |
| (iv) Two sides of equal length | Equilateral triangle |
| (v) All sides are equal | Obtuse angled triangle |
Solution:
| (i) No sides are equal | Scalene triangle |
| (ii) One right angle | Right-angled triangle |
| (iii) One obtuse angle | Obtuse angled triangle |
| (iv) Two sides of equal length | Isosceles triangle |
| (v) All sides are equal | Equilateral triangle |
Question 3.
In ∆ABC, name the
(a) Three sides: ____, _____, _____
(b) Three Angles: _____, _____, _____
(c) Three Vertices: _____, _____, _____
Solution:
(a) \(\overline { AB }\), \(\overline { BC }\), \(\overline { CA }\)
(b) ∠ABC, ∠BCA, ∠CAB or ∠A, ∠B, ∠C
(c) A, B, C
Question 4.
Classify the given triangles based on its sides as scalene, isosceles or equilateral.
Solution:
(i) Equilateral Triangle
(ii) Scalene Triangle
(iii) Isosceles Triangle
(iv) Scalene Triangle
Question 5.
Classify the given triangles based on its angles as acute-angled, right-angled or obtuse-angled.
Solution:
(i) Acute angled triangle
(ii) Right-angled triangle
(iii) Obtuse angled triangle
(iv) Acute angled triangle
Question 6.
Classify the following triangles based on their sides and angles.
Solution:
(i) Isosceles Acute angled triangle
(ii) Scalene Right-angled triangle
(iii) Isosceles Obtuse angled triangle
(iv) Isosceles Right-angled triangle
(v) Equilateral Acute angled triangle
(vi) Scalene Obtuse angled triangle
Question 7.
Can a triangle be formed with the following sides? If yes, name the type of triangle.
(i) 8 cm, 6 cm, 4 cm
(ii) 10 cm, 8 cm, 5 cm
(iii) 6.2 cm, 1.3 cm, 3.5 cm
(iv) 6 cm, 6 cm, 4 cm
(v) 3.5 cm, 3.5 cm, 3.5 cm
(vi) 9 cm, 4 cm, 5 cm
Solution:
(i) 8 cm, 6 cm, 4 cm
Sum of smaller sides = 6 cm + 4 cm = 10 cm > 8 cm, third side
∴ Triangle can be formed with these sides
None of the sides is equal.
∴ Yes, it is a scalene triangle
(ii) 10 cm, 8 cm, 5 cm.
Sum of two smaller sides = 8 cm + 5 cm = 13 cm > 10 cm, third side
∴ Triangle can be formed
None of the sides is equal.
∴ Yes, it is a scalene triangle
(iii) 6.2 cm, 1.3 cm, 3.5 cm.
Here sum of two smaller sides = 1.3 cm + 3.5 cm = 4.8 cm < 6.2 cm, third side.
∴ No, The triangle cannot be formed
(iv) 6 cm, 6 cm, 4 cm
Sum of two smaller sides = 4 cm + 6 cm = 10 cm > 6 cm, third side.
∴ Triangle can be formed. Also two sides are equal.
∴ Yes, it is an isosceles triangle.
(v) 3.5 cm, 3.5cm, 3.5cm.
Here sum of two sides = 3.5 cm + 3.5 cm = 7 cm > 3.5 cm (Third side)
∴ Triangle can be formed.
Also, all three sides are equal.
∴ Yes, it is an equilateral triangle.
(vi) 9 cm, 4 cm, 5 cm.
Sum of two smaller sides = 4 cm + 5 cm = 9 cm (the third side).
∴ No, The triangle cannot be formed
Question 8.
Can a triangle be formed with the following angles? if yes, name the type of triangle.
(i) 60°, 60°, 60°
(ii) 90°, 55°, 35°
(iii) 60°, 40°, 42°
(iv) 60°, 90°, 90°
(v) 70°, 60°, 50°
(vi) 100°, 50°, 30°
Solution:
(i) 60°, 60°, 60°
Sum of three angles = 60° + 60° + 60° = 180°
Yes, a triangle can be formed.
∴ It is Acute angled triangle. [∵ all the angles < 90°]
(ii) 90°, 55°, 35°.
Sum of three angles = 90° + 55° + 55° = 180°
Yes, a triangle can be formed.
∴ It is a right-angled triangle, [∵ one angle is 90°]
(iii) 60°, 40°, 42°.
Sum of three angles = 60° + 40° + 42° = 142° ≠ 180°
No, The triangle cannot be formed.
(iv) 60°, 90°, 90°.
Sum of three angles = 60° + 90° + 90° = 240° ≠ 180°
∴ No, The triangle cannot be formed. [∵ one angle is > 90°]
(v) 70°, 60°, 50°.
Sum of three angles = 70° + 60° + 50° = 180°
Yes, A triangle can be formed.
∴ It is an acute-angled triangle.
(vi) 100°, 50°, 30°.
Sum of three angles = 100° + 50° + 30° = 180°
Yes, A triangle can be formed.
∴ It is an obtuse-angled triangle.
Question 9.
Two angles of the triangles are given. Find the third angle.
(i) 80°, 60°
(ii) 52°, 68°
(iii) 75°, 35°
(iv) 50°, 90°
(v) 120°, 30°
(vi) 55°, 85°
Solution:
(i) 80°, 60°
Sum of the two angles = 80° + 60° = 140°
We know that sum of three angles of a triangle = 180°
Third angle = 180° – 140° = 40°
(ii) 75°, 35°
In the triangle sum of two angles = 75° + 35° = 110°
In a triangle sum of three angles = 180°
Third angle = 180° – 110° = 70°
(iii) 52°, 68°
In a triangle sum of 3 angles = 180°
Here sum of two given angles = 52° + 68° = 120°
Third angle = 180° – 120° = 60°
(iv) 50°, 90°
In a triangle sum of three angles = 180°
Sum of two given angles = 50° + 90° = 140°
Third angle = 180° – 140° = 40°
(v) 120°, 30°
In a triangle sum of three angles = 180°
Sum of two given angles = 120° + 30° = 150°
Third angle = 180° – 150° = 30°
(vi) 55°, 85°
In a triangle sum of three angles = 180°
Sum of two given angles = 55° + 85° = 140°
Third angle = 180° – 140° = 40°
Question 10.
I am a closed figure with each of my three angles is 60°. Who am I?
Solution:
Equilateral Triangle.
Question 11.
Using the given information, write the type of triangle in the table given below.
Solution:
Objective Type Questions
Question 12.
The given triangle is _____.
(a) a right-angled triangle
(b) an equilateral triangle
(c) a scalene triangle
(d) an obtuse-angled triangle
Solution:
(b) an equilateral triangle
Question 13.
If all angles of a triangle are less than a right angle, then it is called ……….
(a) an obtuse-angled triangle
(b) a right-angled triangle
(c) an isosceles right-angled triangle
(d) an acute-angled triangle
Solution:
(d) an acute-angled triangle
Question 14.
If two sides of a triangle are 5 cm and 9 cm then the third side is _____.
(a) 5 cm
(b) 3 cm
(c) 4 cm
(d) 14 cm
Solution:
(a) 5 cm
Question 15.
The angles of a right-angled triangle are
(a) acute, acute, obtuse
(b) acute, right, right
(c) right, obtuse, acute
(d) acute, acute, right
Solution:
(d) acute, acute, right
Question 16.
An equilateral triangle is
(a) an obtuse-angled triangle
(b) a right-angled triangle
(c) an acute-angled triangle
(d) scalene triangle
Solution:
(c) an acute-angled triangle