Question

problem 22: select the converse of this statement and determine whether it is true or false. if two angles of a triangle are congruent (equal), then the sides opposite those angles are congruent (equal).

Explanation:

Step1: Define converse

Switch hypothesis and conclusion.
Given statement: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Converse: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Step2: Recall isosceles - triangle theorem

In an isosceles triangle, if \(AB = AC\) in \(\triangle ABC\), then \(\angle B=\angle C\).
This is a well - known theorem in geometry. So the converse is true.

Answer:

The converse statement is: If two sides of a triangle are congruent (equal), then the angles opposite those sides are congruent (equal). This converse statement is true.