Chapter 2.1, Problem 29WE

To determine

To state: A definition of congruent angles as a biconditional

Answer to Problem 29WE

The bi-conditional statement is:

  $\angle R\cong \angle S$ if and only if $m\angle R=m\angle S$

Explanation of Solution

Given information:

The angles are congruent

Congruent angles are angles that have equal measures.

Let $\angle R$ and $\angle S$ both have equal measure then:

  $\angle R\cong \angle S$ or $m\angle R=m\angle S$

The definition of congruent angles tells us that these two statements are equivalent

Therefore, the bi-conditional statement is:

  $\angle R\cong \angle S$ if and only if $m\angle R=m\angle S$