Question

A Use the conditional statement below to answer each question. "If a polygon is regular, then all of its angles are congruent."

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

Answer 1

The converse, inverse, and contrapositive of the conditional statement "If a polygon is regular, then all of its angles are congruent" are, respectively: "If all of a polygon's angles are congruent, then the polygon is regular," "If a polygon is not regular, then not all of its angles are congruent," and "If not all of a polygon's angles are congruent, then the polygon is not regular."

Step-by-step explanation:

The conditional statement given is "If a polygon is regular, then all of its angles are congruent."

• The converse of the conditional statement would be "If all of a polygon's angles are congruent, then the polygon is regular."
• The inverse of the conditional statement would be "If a polygon is not regular, then not all of its angles are congruent."
• The contrapositive of the conditional statement would be "If not all of a polygon's angles are congruent, then the polygon is not regular."

These logical forms are useful for constructing valid arguments and understanding relationships between propositions in fields like mathematics and philosophy.