If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle. Can you say that two triangles will be similar? Why?

Question

Philoid · Accepted Answer

(True)

Let two right angled triangles be,

∆LMO and ∆RST

In which

∠L = ∠R = 90°

And

∠M = ∠S [Acute angle]

By angle sum property of triangle that, sum of interior angles of a triangle is 180°. Angle O of first triangle must be equal to angle T of second triangle.

So,

∠O = ∠T

Hence, by AAA similarity criteria,

We have, ∆LMO ∼ ∆RST