# WORKSHEET ON TYPES OF TRIANGLES

1. Identify the type of triangle whose angles are 35°, 40° and 105°.

2. Identify the type of triangle whose angles are 55°, 65° and 60°.

3. Identify the type of triangle whose angles are 50°, 40° and 90°.

4. Identify the type of triangle whose angles are 45°, 45° and 90°.

5. Identify the type of triangle whose angles are 70°, 70° and 40°.

6. Identify the type of triangle whose angles are 30°, 30° and 120°.

7. Identify the type of triangle whose sides are 5 cm, 6 cm and 7 cm.

8. Identify the type of triangle whose sides are 6 cm, 6 cm and 8 cm.

9. If (3x + 3)° is one of the angles of an acute triangle, then find the value of x.

10. If 50°, 40° and (2x + 4)°are the angles of a right triangle, then find the value of x

11. If (2x)°, y° and (3z)° are the angles of a acute triangle, find the value of z.

12. If (2x + 15°, (3x)° and (6x)° are the angles of a triangle, identify type of the triangle.

13. The sides of a triangle are 6cm, 8cm and 10cm. Check whether it is a right triangle.

14. The sides of a triangle are 5in, 5in and 5√2in. Check whether it is a right triangle.

(i) All the given three angles are different

(ii) One of the angles is greater than 90°

So, the given triangle is a scalene and obtuse triangle.

(i) All the given three angles are different

(ii) All the three angles are less than 90°

So, the given triangle is a scalene and acute triangle.

(i)  All the given three angles are different

(ii)  One of the angles is 90°

So, the given triangle is a scalene and right triangle.

(i)  Two of the given angles are equal

(ii)  One of the angles is 90°

So, the given triangle is an isosceles and right triangle.

(i)  Two of the given angles are equal

(ii)  All the three angles are less than 90°

So, the given triangle is an isosceles and acute triangle.

(i)  Two of the given angles are equal

(ii)  One of the angles is greater than 90°

So, the given triangle is an isosceles and obtuse triangle.

The length of all the three sides are different.

So, the given triangle is a scalene triangle.

The lengths of two of the sides are equal.

So, the given triangle is an isosceles triangle.

Since the given triangle is acute triangle, all the three angles will be less than 90°.

So, (3x + 3)° will also be less than 90°.

3x + 3 < 90

3x < 87

x < 29

Since the given triangle is a right triangle, one of the angles must be 90°.

In the given three angles 50°, 40° and (2x+4)°, the first two angles are not right angles.

So the third angle (2x + 4)° must be right angle.

2x + 4 = 90

2x = 86

x = 43

Since the given triangle is acute triangle, all the three angles will be less than 90°.

So, (3z)° will also be less than 90°.

(3z)° < 90°

3z < 90

z < 30

Since (2x + 15)°, (3x)° and (6x)° are the angles of a triangle, by property.

(2x + 15)° + (3x)° + (6x)° = 180°

2x + 15 + 3x + 6x = 180

11x + 15 = 180

11x = 165

x = 15

Substitute x = 15.

First angle = 2x + 15 = 2(15) + 15 = 45°

Second angle = 3x = 3(15) = 45°

Third angle = 6x = 6(15) = 90°

Let us consider the following two important points from the above calculation.

(i) Two of the angles are equal

(ii) One of the angles is 90°

So, the given triangle is an isosceles and right triangle.

Given : the sides of a triangle are 6cm, 8cm and 10cm.

62 = 36, 82 = 64, 102 = 100

36 + 64 = 100

62 + 82 = 102

Sum of squares of two sides is equal to square of the third side.

The given sides satisfies Pythagorean Theorem. So the given triangle is a right triangle.

Given : The sides of a triangle are 5in, 5in and 5√2in.

52 = 25, 52 = 25, (5√2)2 = 50

25 + 25 = 50

52 + 52 = (5√2)2

Sum of squares of two sides is equal to square of the third side.

The given sides satisfies Pythagorean Theorem and also two of its sides are equal. So the given triangle is an isosceles right triangle.

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