Question

Write the following statement as a biconditional:

If two angles are vertical angles, then they are congruent
(1 point)
Two angles are not vertical if and only if they are not
congruent.
Two angles are vertical angles if and only if they are
congruent.
If two angles are not vertical angles, then they are not
congruent
If two angles are congruent, then they are vertical angles

Answer 1

Two angles are vertical angles if and only if they are congruent.

Explanation:

A biconditional statement is a statement that combines a conditional statement and its converse, using the phrase "if and only if." In this case, the original statement is "If two angles are vertical angles, then they are congruent." To convert this into a biconditional statement, we need to include the converse as well. The converse of the original statement is "If two angles are congruent, then they are vertical angles."

Combining the original statement and its converse, we get the biconditional statement:

Two angles are vertical angles if and only if they are congruent.

Answer 2

Two angles are vertical angles if and only if they are congruent.

In a biconditional statement, both the conditional and the converse must be true. In this case, the original statement “If two angles are vertical angles, then they are congruent” can be rewritten as a biconditional statement: “Two angles are vertical angles if and only if they are congruent.”

This means that if two angles are vertical angles, then they are also congruent, and conversely, if two angles are congruent, then they are also vertical angles.

Therefore, the correct biconditional statement for the given statement is: “Two angles are vertical angles if and only if they are congruent.”

Hope this helped.