Question

Write a definition of congruent angles as a biconditional.

Short answer

The definition of congruent angles as a biconditional is: “$\angle A\cong \angle B$ if and only if $m\angle A=m\angle B$”.

Step-by-step solution

Step 1. Define the congruent angles.

Congruent angles are angles that have equal measures.

Let$\angle A$ and$\angle B$ both have equal measure then:

$\angle A\cong \angle B$or $m\angle A=m\angle B$.

Step 2. Define the biconditional.

If a conditional and its converse are both true then they can be combined into a single statement by using connector “if and only if”. Such a statement containing the words “if and only if” is defined as a biconditional. For example, “p if and only if q”.

Step 3. Write the biconditional for the definition of congruent angles.

The definition of congruent angles tells us that the two statements$\angle A\cong \angle B$ or $m\angle A=m\angle B$are equivalent.

Therefore, the bi-conditional statement is:

$\angle A\cong \angle B$if and only if $m\angle A=m\angle B$.