Question

drag the tiles to the boxes to form correct pairs. determine which statements are the converse, inverse, and contrapositive of the following statement. if a figure is a square, it is a polygon. if a figure is a polygon, it is not a square. if a figure is not a polygon, it is not a square. if a figure is a square, it is not a polygon. if a figure is not a square, it is not a polygon. if a figure is a polygon, it is a square. converse inverse contrapositive

Explanation:

Step1: Recall the definitions

For a conditional statement "If \(p\), then \(q\)", the converse is "If \(q\), then \(p\)", the inverse is "If not \(p\), then not \(q\)" and the contra - positive is "If not \(q\), then not \(p\)". The original statement is "If a figure is a square, it is a polygon", where \(p\) = "a figure is a square" and \(q\) = "a figure is a polygon".

Step2: Find the converse

The converse swaps the hypothesis and conclusion. So the converse is "If a figure is a polygon, it is a square".

Step3: Find the inverse

The inverse negates both the hypothesis and conclusion. So the inverse is "If a figure is not a square, it is not a polygon".

Step4: Find the contra - positive

The contra - positive negates and swaps the hypothesis and conclusion. So the contra - positive is "If a figure is not a polygon, it is not a square".

Answer:

Converse: If a figure is a polygon, it is a square.
Inverse: If a figure is not a square, it is not a polygon.
Contrapositive: If a figure is not a polygon, it is not a square.