Page 159 - Math Skill - 5

Geometry 157

Let’s Attempt

Example 1: Is it possible to form a triangle whose sides are 4 cm, 5 cm and 10 cm?

Solution: According to the property of triangles, if sum of the lengths of any two sides is
greater than the length of the third side, then a triangle is possible.

Here 5 cm + 4 cm = 9 cm < 10 cm
Hence, the triangle is not possible.

Example 2: In ∆PQR, ∠P = 55° and ∠Q = 65°, find ∠R.

Solution: According to the angle sum property, the sum of all the angles of a triangle is 180°.

So, ∠P + ∠Q + ∠R = 180°
55° + 65° + ∠R = 180°

120° + ∠R = 180°

\ ∠R = 180° – 120° = 60°

Hence, ∠R = 60°.
Example 3: Which of the following cannot be the measures of the three angles of a triangle?

(a) ∠P = 30°, ∠Q = 135°, ∠R = 20°

(b) ∠L = 40°, ∠M = 50°, ∠N = 90°
Solution: (a) ∠P + ∠Q + ∠R = 30° + 135° + 20° = 185°

The sum is greater than 180°, the triangle is not possible.

(b) ∠L + ∠M + ∠N = 40° + 50° + 90° = 180°
The sum is equal to 180°, the triangle is possible.

Example 4: One of the two equal angles of an isosceles triangle measures 45°. Find all the
three angles.

Solution: Sum of two equal angles of an isosceles triangle = 45° + 45° = 90°

Sum of three angles = 180°
Third angle = 180° – 90° = 90°

Hence, all the three angles are 45°, 45° and 90°.

Exercise 12.4

1. Fill in the blanks.
(a) In a scalene triangle, all the three sides are of ________ lengths.

(b) Each angle of an equilateral triangle measures ________.
(c) ________ sides of an isosceles triangle are ________ in length.