Exercise 4.1

Exercise 4.1

1. Fill in the blanks:

a) Every triangle has at least two acute angles.

b) A triangle in which none of the sides equal is called a Scalene triangle.

c) In an isosceles triangle two angles are equal.

d) The sum of three angles of a triangle is 180°.

e) A right angled triangle with two equal sides is called Isosceles right angled triangle.

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

Answer

(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 

3. In ΔABC, name the

 a) Three sides: ______ , ______ , _______

b) Three Angles: ______ , ______ , _______

c) Three Vertices: ______ , _______ , _______

a) Three sides : 

b) Three Angles :  ∠ABC, ∠BCA, ∠CAB

c) Three Vertices : A, B, C

4. Classify the given triangles based on its sides as scalene, isosceles or equilateral.

Answer:

(i) Equilateral triangle

(ii) Scalene triangle

(iii) Isoceles triangle

(iv) Scalene triangle

5. Classify the given triangles based on its angles as acute angled, right angled or obtuse angled.

Answer:

(i) Acute angled triangle

(ii) Right angled triangle

(iii) Obtuse angled triangle

(iv) Acute angled triangle

6. Classify the following triangles based on its sides and angles.

Answer:

(i) Isoceles acute angled triangle

(ii) Scalene right angled triangle

(iii) Isoceles obtuse angled triangle

(iv) Isoceles right angled triangle

(v) Equilateral acute angled triangle

(vi) Scalene obtuse angled triangle

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

(i) 8 cm, 6 cm, 4 cm

The sum of two smaller sides = 6 + 4 = 10 cm > 8 cm, the third side.

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

It is scalene triangle.

(ii) 10 cm, 8 cm, 5 cm

The sum of two smaller sides = 8 + 5 = 13 cm > 10 cm, the third side.

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

It is scalene triangle.

(iii) 6.2 cm, 1.3 cm, 3.5 cm

The sum of two smaller sides = 1.3 + 3.5 = 4.8 cm < 6.2 cm the third side.

The sum of two smaller sides is lesser than the third side.

So, a triangle can not be formed with the given sides.

(iv) 6 cm, 6 cm, 4 cm

The sum of two smaller sides = 6 + 4=10 cm > 6 cm, the third side

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

It is Isosceles triangle.

(v) 3.5 cm, 3.5 cm, 3.5 cm

The three sides are equal, so definitely a triangle can be formed, as the triangle in equality is satisfied. It is equilateral triangle.

(vi) 9 cm, 4 cm, 5 cm

The sum of two smaller sides = 4 + 5 = 9 cm, the third side.

The sum of two smaller sides is not greater than the third side.

So, a triangle can not be formed with the given sides.

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°

(i) 60°, 60°, 60°

The sum of three angles = 60° + 60° + 60° = 180°

So, a triangle can be formed with the given angles.

It is acute angled triangle.

(ii) 90°, 55°, 35°

The sum of three angles = 90° + 55° + 35° = 180°

So, a triangle can be formed with the given angles.

It is right angled triangle.

(iii) 60°, 40°, 42°

The sum of three angles = 60° + 40° + 42° = 142° ≠ 180°

So, a triangle can not be formed with the given angles.

(iv) 60°, 90°, 90°

The sum of three angles = 60° + 90° + 92° = 240° ≠ 180°

So, a triangle can not be formed with the given angles.

(v) 70°, 60°, 50°

The sum of three angles = 70° + 60° + 50° = 180°

So, a triangle can be formed with the given angles.

It is acute angled triangle. 

(vi) 100°, 50°, 30°

The sum of three angles = 100° + 50° + 30° = 180°

So, a triangle can be formed with the given angles.

It is obtuse angled triangle.

9. Two angles of the triangles are given. Find the third angle.

(i) 80° , 60°

(ii) 75° , 35°

(iii) 52° , 68°

(iv) 50° , 90°

(v) 120° , 30°

(vi) 55° , 85°

(i) 80°, 60°

The two angles 80°, 60°

The sum of three angles = 180°

The sum of two angles = 80° + 60° = 140°

The third angle = The sum of three angles − The sum of two angles

= 180°− 140° = 40°

(ii) 75°, 35°

The two angles 75°, 35°

The sum of three angles = 180°

The sum of two angles = 75° + 35° = 110°

The third angle = The sum of three angles − The sum of two angles

= 180°− 110° = 70°

(iii) 52°, 68°

The two angles 52°, 68°

The sum of three angles = 180°

The sum of two angles = 52° + 68° = 120°

The third angle = The sum of three angles − The sum of two angles

= 180°− 120° = 60°

(iv) 50°, 90°

The two angles 50°, 90°

The sum of three angles = 180°

The sum of two angles = 50° + 90° = 140°

The third angle = The sum of three angles − The sum of two angles

= 180°− 140° = 40° 

(v) 120°, 30°

The two angles 120°, 30°

The sum of three angles = 180°

The sum of two angles = 120° + 30° = 150°

The third angle = The sum of three angles − The sum of two angles

= 180° − 150° = 30°

(vi) 55°, 85°

The two angles 55°, 85°

The sum of three angles = 180°

The sum of two angles = 55° + 85° = 140°

The third angle = The sum of three angles − The sum of two angles

= 180° − 140° = 40°

10. I am a closed figure with each of my three angles is 60° . Who am I?

I am an equilateral triangle.

11. Using the given information, write the type of triangle in the table given below

Answer:

Objective Type Questions

12. The given triangle is _______.

a) a right angled triangle

b) an equilateral triangle

c) a scalene triangle

d) an obtuse angled triangle

Answer: b) an equilateral triangle

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

Answer: d) an acute angled triangle

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

Answer: a) 5 cm

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

Answer: d) acute, acute, right

16. An equilateral triangle is

a) an obtuse angled triangle

b) a right angled triangle

c) an acute angled triangle

d) a scalene triangle

Answer: c) an acute angled triangle

ANSWERS:

Exercise 4.1

1. a) two b) scalene triangle c) two d) 180° e) isosceles right angled triangle

2. i) Scalene triangle

ii) Right angled triangle

iii) Obtuse angled triangle

iv) Isosceles triangle

v) Equilateral triangle

3. a) 

b) ∠ABC, ∠BCA, ∠CAB or ∠A, ∠B, ∠C

c) A, B, C

4. i) Equilateral triangle ii) Scalene triangle iii) Isosceles triangle iv) Scalene triangle

5. i) Acute angled triangle

ii) Right angled triangle

iii) Obtuse angled triangle

iv) Acute angled triangle

6. i) a) Isosceles Acute angled triangle

ii) a) Scalene Right -angled triangle

iii) a) Isosceles Obtuse angled triangle

iv) a) Isosceles Right -angled triangle

v) a) Equilateral Acute angled triangle

vi) a) Scalene Obtuse angled triangle

7. i) Yes, Scalene triangle

ii) Yes, Scalene triangle

iii) No, The triangle cannot be formed

iv) Yes, Isosceles triangle

v) Yes, Equilateral triangle

vi) No, The triangle cannot be formed

8. i) Yes, Acute angled triangle

ii) Yes, Right angled triangle

iii) No, The triangle cannot be formed

iv) No, The triangle cannot be formed

v) Yes, Acute angled triangle

vi) Yes, Obtuse angled triangle

9. i) 40° ii) 70° iii) 60° iv) 40° v) 30° vi) 40°

10. Equilateral Triangle

11. ii) Acute angled triangle, Isosceles triangle

iii) Right angled triangle, Isosceles triangle

iv) Acute angled triangle, Scalene triangle

v) Acute angled triangle, Scalene triangle

vi) Right angled triangle, Scalene triangle

vii) Obtuse angled triangle, Scalene triangle

viii) Obtuse angled triangle, Isosceles triangle

Objective Type Questions

12. b

13. d

14. a

15. d

16. c