Question

write the contrapositive of the conditional statement.

if a polygon is regular, then it has congruent angles and congruent sides.

if a polygon has congruent angles and congruent sides, then it is regular.

if a polygon does not have congruent angles and congruent sides, then it is not regular.

a polygon has congruent angles and congruent sides, if and only if, it is regular.

if a polygon is not regular, then it does not have congruent angles and congruent sides.

Explanation:

Step1: Recall contrapositive definition

The contrapositive of a conditional statement \( p \to q \) is \(
eg q \to
eg p \), where \( p \) is the hypothesis and \( q \) is the conclusion.
Here, \( p \): "a polygon is regular", \( q \): "it has congruent angles and congruent sides".

Step2: Find \(

eg q \) and \(
eg p \)
\(
eg q \): "a polygon does not have congruent angles and congruent sides", \(
eg p \): "it is not regular".

Step3: Form contrapositive

Using \(
eg q \to
eg p \), the contrapositive is "If a polygon does not have congruent angles and congruent sides, then it is not regular".

Answer:

If a polygon does not have congruent angles and congruent sides, then it is not regular.