Exercise 4.3

Exercise 4.3

Miscellaneous Practice Problems

1. What are the angles of an isosceles right angled triangle?

45°, 45°, 90°

2. Which of the following correctly describes the given triangle?

(a) It is a right isosceles triangle.

(b) It is an acute isosceles triangle.

(c) It is an obtuse isosceles triangle.

(d) It is an obtuse scalene triangle.

Answer: ✓(c) It is an obtuse isosceles triangle.

3. Which of the following is not possible ?

(a) An obtuse isosceles triangle

(b) An acute isosceles triangle

(c) An obtuse equilateral triangle

(d) An acute equilateral triangle

Answer: ✓(c) An obtuse equilateral triangle 

4. If one angle of an isosceles triangle is 124° , then find the other angles.

One angle of an isosceles triangle = 124°

The sum of three angles of a triangle = 180°

The other two isosceles angles = 180° − 124° = 56°

One angle = 56 / 2 = 28°

The other two angles are 28°, 28°.

5. The diagram shows a square ABCD. If the line segment joins A and C, then mention the type of triangles so formed.

Both triangles are Isoceles Right angled triangle.

6. Draw a line segment AB of length 6 cm. At each end of this line segment AB, draw a line perpendicular to the line AB. Are these lines parallel?

Yes. These two perpendicular lines are parallel.

Challenge Problems

7. Is a triangle possible with the angles 90° , 90° and 0° Why?

90°, 90°, 0°

A triangle can not be formed with the given angles. Because, Atriangle can not have more than one right angle.

8. Which of the following statements is true? Why?

(a) Every equilateral triangle is an isosceles triangle.

(b) Every isosceles triangle is an equilateral triangle.

'a' is true. Because an isosceles triangle need not have three equal sides.

9. If one angle of an isosceles triangle is 70°, then find the possibilities for the other two angles.

One angle of an isosceles triangle = 70°

If the other angle also = 70°

The third angle = 180° − (70° + 70°)

= 180° − 140° = 40°

The other two angles are 70° and 40° (or)

One angle = 70°

The other two isosceles angles = (180° − 70°) = 110°

Two isosceles angles = 110°

So, one angle = 110 / 2 = 55°

The other two isosceles angles are 55° and 55°

So, the two angles 70°, 40° (or) may be, 55°, 55°..

10. Which of the following can be the sides of an isosceles triangle?

a) 6cm, 3cm, 3cm

b) 5cm, 2cm, 2cm

c) 6cm, 6cm, 7cm

d) 4cm, 4cm, 8cm

a) 6 cm, 3 cm, 3 cm

The sum of two smaller sides = 3+3 = 6cm=6cm, 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.

b) 5 cm, 2 cm, 2 cm

The sum of two smaller sides=2 + 2 = 4 cm < 5 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.

c) 6 cm, 6 cm, 7 cm

The sum of two smaller sides = 6 + 6 = 12 cm > 7 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.

d) 4 cm, 4 cm, 8 cm

The sum of two smaller sides = 4 + 4 = 8 cm = 8 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.

11. Study the given figure and identify the following triangles.

(a) equilateral triangle

(b) isosceles triangles

(c) scalene triangles

(d) acute triangles

(e) obtuse triangles

(f) right triangles

(a) Equilateral triangle

Equilateral triangle ΔABC

(b) Isosceles triangles

Isosceles triangle Δ ABC, Δ AEF

(c) Scalene triangles

Scalene triangle Δ AEB, Δ AED, Δ ADF, Δ AFC, Δ ABD, Δ ADC, Δ ABF, Δ AEC

(d) Acute triangles

Acute triangles Δ ABC, Δ AEF, Δ ABF, Δ AEC

(e) Obtuse triangles

Obtuse triangles Δ AEB, Δ AFC

(f) Right triangles

Right triangles Δ ADB, Δ ADC, Δ ADE, Δ ADF

12. Two sides of the triangle are given in the table. Find the third side of the triangle.

i) 7cm, 4 cm

The sum of two smaller sides = 4 + 4 = 8 cm > 7 cm, the third side

= 4 + 5 = 9 cm > 7 cm, the third side

= 4 + 6 = 10 cm > 7 cm, the third side

The third side is, 4 cm or 5 cm or 6 cm.

ii) 8 cm, 8 cm

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

= 6 + 8 = 14 cm > 8 cm, the third side

= 7 + 8 = 15 cm > 8 cm, the third side

The third side is, 5 cm or 6 cm or 7 cm. 

iii) 7.5 cm, 3.5 cm

The sum of two smaller sides = 3.5 + 4.5 = 8cm > 7.5 cm, the third side  

= 3.5 + 5 = 8.5 cm > 7.5 cm, the third side

= 3.5 + 6 = 9.5 cm > 7.5 cm, the third side

The third side is 4.5 cm or 5 cm or 6 cm

iv. 10 cm, 14 cm

The sum of two smaller sides = 10 + 5= 15 cm> 14 cm, the third side

= 10 + 7 = 17cm > 14 cm, the third side

= 10 + 8 = 18 cm > 14 cm, the third side

The third side is 5 cm or 7 cm or 8 cm

13. Complete the following table :

ANSWERS:

Exercise 4.3

1. 90°, 45° , 45°

2. c

3. c

4. 28°, 28°

5. Both are Isosceles Right angled triangles

6. Yes

7. No, A triangle cannot have more than one right angle

8. “a” is true, because an isosceles triangle need not have three equal sides

9. 70°,40° or 55°,55°

10. c

11. a) ∆ABC

b) ∆ABC , ∆AEF

c) ∆AEB, ∆AED, ∆ADF, ∆AFC, ∆ABD, ∆ADC, ∆ABF, ∆AEC

d) ∆ABC, ∆AEF, ∆ABF, ∆AEC

e) ∆AEB, ∆AFC

f) ∆ADB, ∆ADC, ∆ADE, ∆ADF

12. (i) between 3 and 11   (ii) between 0 and 16   (iii) between 4 and 11  (iv) between 4 and 24

13. i .Always acute angles

 ii. Acute angle

 iii. Obtuse angle