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  • 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?

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?

Answers (1)

Answer : [True]

Let two right angle triangles are ABC and PQR.

Given:- One of the acute angle of one triangle is equal to an acute angle of the other triangle.

\text {In}\Delta ABC \; \text {and}\; \Delta PQR

\\\angle B = \angle Q = 90^{o}\\\angle C = \angle R = x^{o}                         

In \Delta ABC

\angle A + \angle B + \angle C = 180^{o}          

[Sum of interior angles of a triangle is 180°]

\angle A + 90^{o}+ x^{o} = 180^{o}

\angle A + 90^{o}- x^{o} \; \; \; \; \; \; \; \; \; ....(1)

Also in \Delta PQR

\angle P + \angle Q + \angle R = 180^{o}

\angle P + 90^{o}- x^{o} = 180^{o}

\angle P = 90^{o}- x^{o} \; \; \; \; \; \; .....(2)

from equation (1) and (2)

\angle A=\angle P \; \; \; \; \; \; .....(3)

from equation (1), (2) and (3) are observed that corresponding angles of the triangles are equal therefore triangle are similar.

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infoexpert23

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