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Expert-verified Found in: Page 35 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Write a definition of congruent angles as a biconditional.

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

See the 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 $m\angle A=m\angle B$. ### Want to see more solutions like these? 