Question

read the false statement below and then tell whether the converse, inverse, and contrapositive are true. if a figure is not a parallelogram, then it is not a polygon. converse inverse contrapositive if a figure is not a polygon, then it is not a parallelogram. true false

Explanation:

Step1: Analyze the converse

The converse is “If a figure is not a polygon, then it is not a parallelogram.” A parallelogram is a type of polygon. So if a figure is not a polygon, it can't be a parallelogram. This is true.

Step2: Analyze the inverse

The original statement is “If \(p\) (a figure is not a parallelogram), then \(q\) (it is not a polygon)”. The inverse is “If not \(p\) (a figure is a parallelogram), then not \(q\) (it is a polygon)”. A parallelogram is a polygon. So the inverse is true.

Step3: Analyze the contrapositive

The contrapositive of “If \(p\), then \(q\)” is “If not \(q\), then not \(p\)”. The contrapositive is “If a figure is a polygon, then it is a parallelogram”. There are many polygons (like triangles, trapezoids) that are not parallelograms. So the contrapositive is false.

Answer:

Converse: True; Inverse: True; Contrapositive: False