Draw an isosceles right triangle of hypotenuse 4 centimetres.

Question

Philoid · Accepted Answer

1) Draw a line BC 4 cm.

2) At B, draw ∠XBC = 45°

3) At C, draw ∠YCB = 45°

BX and CY intersect each other at A. and ΔABC is required triangle,

Also,

In ΔABC

∠B = ∠C = 45°

Therefore, AB = AC [i.e. ABC is isosceles]

And By angle sum property of triangle,

∠A + ∠B + ∠C = 180°

⇒ ∠A + 45 + 45 = 180

⇒ ∠A = 90°

Hence, ABC is isosceles.