Question

select the statement that is the inverse of the following statement: if a rectangle has four congruent sides, then it is a square. answer: if a rectangle has four congruent sides, then it isnt a square. if a rectangle is a square, then it has four congruent sides. if a rectangle isnt a square, then it doesnt have four congruent sides. if a rectangle doesnt have four congruent sides, then it isnt a square.

Explanation:

Step1: Recall the definition of inverse statement

The inverse of a conditional statement "If \( p \), then \( q \)" is "If not \( p \), then not \( q \)". Here, the original statement is "If a rectangle has four congruent sides (\( p \)), then it is a square (\( q \))". So the inverse should be "If a rectangle does not have four congruent sides (not \( p \)), then it is not a square (not \( q \))".

Step2: Analyze each option

• Option 1: "If a rectangle has four congruent sides, then it isn't a square" - This is not the inverse (it negates \( q \) but not \( p \)).
• Option 2: "If a rectangle isn't a square, then it doesn't have four congruent sides" - This is the contrapositive (negates and reverses \( p \) and \( q \)), not the inverse.
• Option 3: "If a rectangle is a square, then it has four congruent sides" - This is the converse (reverses \( p \) and \( q \)), not the inverse.
• Option 4: "If a rectangle doesn't have four congruent sides, then it isn't a square" - This matches the form of the inverse (not \( p \) implies not \( q \)).

Answer:

If a rectangle doesn't have four congruent sides, then it isn't a square.