Question

1. If one angle of a triangle is equal to the sum of the other two, show the triangle is a right triangle.

Answer 1

Let
ABC is a triangle,in which angle B is equal to the sum of angle A and angle C.

So,In triangle ABC,

angle B = angle A+angle C -------------------->(1)

Now, we know that,

angle A+ angle B+ angle C = 180°

=>angle B+(angle A+angle C) = 180°

=> angle B+angle B = 180° [From (1)]

=> 2 angle B = 180°

=> angle B = 180°/2

=> angle B = 90°


If one angle of a triangle is90°,the triangle is known as right triangle.

So,ABC is a right triangle.
Proved.