Question

a statement is shown.
if a polygon has four congruent sides and four right angles, then it is a square.
which is the contrapositive of the statement?

○ if a polygon is a square, then it has four congruent sides and four right angles.
○ if a polygon is a not a square, then it has four congruent sides and four right angles.
○ if a polygon is a not a square, then it does not have four congruent sides and four right angles.
○ if a polygon has does not have four congruent sides and four right angles, then it is not a square.

Explanation:

Step1: Recall the contrapositive rule

For a conditional statement \( p \to q \), the contrapositive is \(
eg q \to
eg p \), where \( p \) is the hypothesis and \( q \) is the conclusion.

Step2: Identify \( p \) and \( q \) in the given statement

The given statement is "If a polygon has four congruent sides and four right angles, then it is a square". So, \( p \): "a polygon has four congruent sides and four right angles", \( q \): "it is a square".

Step3: Find \(

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

Step4: Form the contrapositive

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

Answer:

If a polygon is not a square, then it does not have four congruent sides and four right angles.