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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