Question

Use the conditional statement below to answer each question.

“If two angle measures add up to 90 degrees, then the angles are complementary.”

Write the converse, inverse, and contrapositive of the given conditional statement.

Can the conditional be written as a biconditional statement? Why or why not. Support your answer.

Answer 1

Explanation:

Converse: If two angles are complementary, then the angle measures add up to 90 degrees.

Inverse: If two angle measures don't add up to 90 degrees, then the angles are not complementary.

Contrapositive: If two angles are not complementary, the two angle measures do not add to 90 degrees.

This can be written as a biconditional statement because there is no other case for which two angles will be complementary - this is only possible if their angle measures add to 90 degrees.