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 the two triangles will be similar? Why?

Given:

In two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle.

To do:

We have to find whether the two triangles are similar.

Solution:

Let in two right angled triangles $ABC$ and $PQR$,

$\angle B = \angle Q = 90^o$ and $\angle C = \angle R$

Therefore,

By  angle sum property of triangles,

The sum of the interior angles of a triangle is $180^o$.

This implies,

$\angle A+\angle B+\angle C=\angle P+\angle Q+\angle R$

$\angle A=\angle P$

Therefore, by AA similarity,

$\triangle ABC \sim \angle PQR$.

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Updated on: 10-Oct-2022

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