A day full of math games & activities. Find one near you.

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

Solution:

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

We have to check if the two triangles are similar.

Let the two right triangles be △ABC and △DEF

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

From the above figure,

∠B = ∠E = 90°

Acute angles, ∠A = ∠D

We know that the sum of all the three interior angles of a triangle is always equal to 180°

In △ABC,

∠A + ∠B + ∠C = 180°

∠A + 90° + ∠C = 180°

∠A + ∠C = 180°-90°

∠C = 90° - ∠A

In △DEF,

∠D + ∠E + ∠F = 180°

∠D + 90° + ∠F = 180°

∠D + ∠F = 180°- 90°

∠F = 90° - ∠D

AAA criterion states that if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

As, ∠A = ∠D

∠E = 90° - ∠A

So, ∠E = ∠C

It is clear that the corresponding angles are equal and the corresponding sides are equal.

Therefore, the two right triangles are similar.

✦ Try This: If in two right triangles, two sides of one triangle is proportional to two sides of the other triangle, can you say that the two triangles will be similar? Why

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 8

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

Summary:

If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then the two triangles are similar by AAA criterion

☛ Related Questions: