Chapter 7.4, Problem 9CE

To determine

To Find: whether the two triangles are similar or not if one right triangle has an angle measure $37$ and another right triangle has an angle with measure $53$ .

Answer to Problem 9CE

triangles are similar.

Explanation of Solution

Given:

One right triangle has an angle measure $37$ and another right triangle has an angle with measure $53$ .

Calculation:

Right triangles are shown below.

  

In a triangle sum of three angles is $180$ .

In first triangle ABC.

  $\begin{array}{l}\angle A+\angle B+\angle C=180\\ 37+90+\angle C=180\\ \angle C=180-90-37\\ \angle C=53\end{array}$

In second triangle PQR.

  $\begin{array}{l}\angle P+\angle Q+\angle R=180\\ \angle P+90+53=180\\ \angle P=180-90-53\\ \angle P=37\end{array}$

Since,

  $\begin{array}{l}\angle A=\angle P=37\\ \angle C=\angle R=53\\ \angle B=\angle Q=90\end{array}$

Therefore, by AAA Postulate triangles are similar.

Therefore answer is triangles are similar.