Chapter 2.1, Problem 22WE

To determine

To state: The converse of statement and state whether it is true or false

Answer to Problem 22WE

The statement is true.

The converse of the given statement is true

Explanation of Solution

Given information:

The given statement is:

"If $\angle A\cong \angle B$ then $m\angle A=m\angle B″$

"If $\angle A\cong \angle B$ then $m\angle A=m\angle B″$

Here $\angle A\cong \angle B$

Then $m\angle A=m\angle B$

Therefore, the statement is true.

Consider $p$ is $″\angle A\cong \angle B″$ and $q$ is $″m\angle A=m\angle B″$

The converse is of the form "if $q$ ,then $p^{″}$

Therefore, the converse of the given statement is;

If $m\angle A=m\angle B,$ then $\angle A\cong \angle B$

This is also true because the definition of congruent angles tells us that these two statements are equivalent.

Therefore, the converse of the given statement is true.