Question

Write a definition of a right angle as a biconditional.

Short answer

The definition of congruent angles as a biconditional is: “$\angle R$ is a right angle if and only if $m\angle R={90}^{\circ }$”.

Step-by-step solution

Step 1. Define the right angle.

The right angle is an angle that has measure ${90}^{\text{o}}$.

Let$\angle R$ measure $90°$then, the angle$\angle R$ is a right angle.

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 right angles.

The definition of congruent angles tells us that the two statements$\angle R$ measure$90°$ or the angle$\angle R$ is a right angle. are equivalent.

Therefore, the bi-conditional statement is:

$\angle R$is a right angle if and only if $m\angle R=90°$.