Question

Write the biconditional as two conditionals that are converse of each other:

Angles are congruent if and only if their measures are equal.

Short answer

The conditionals that are converse of each other are:

Angles are congruent or equal if their measures are alike.

Measures of angles are equal if they are congruent.

Step-by-step solution

Step 1. State the biconditional statement.

Angles are congruent if and only if their measures are equal.

Step 2. Define a biconditional statement.

A biconditional statement is the combination of a conditional statement and its opposite written in if and only if form.

Step 3. State the conclusion.

The biconditional statement is “Angles are congruent if and only if their measures are equal”.

Therefore, this statement can be written as a combination of two conditional statements written as follows:

Angles are congruent or equal if their measures are alike.

Measures of angles are equal if they are congruent.