Question

read the true statement below and then tell whether the converse, inverse, and contrapositive are also true.
if a figure is a rhombus, then it is a parallelogram.
converse
if a figure is a parallelogram, then it is a rhombus.

Explanation:

Step1: Analyze the converse

A parallelogram has opposite sides parallel. A rhombus is a parallelogram with all sides equal. But not all parallelograms have all sides equal. So the converse “If a figure is a parallelogram, then it is a rhombus” is false.

Step2: Analyze the inverse

The inverse of “If \(p\) (a figure is a rhombus), then \(q\) (it is a parallelogram)” is “If not \(p\), then not \(q\)”. A non - rhombus (e.g., a rectangle that is not a rhombus) can still be a parallelogram. So the inverse is false.

Step3: Analyze the contrapositive

The contrapositive of “If \(p\), then \(q\)” is “If not \(q\), then not \(p\)”. If a figure is not a parallelogram (i.e., it doesn't have both pairs of opposite sides parallel), then it can't be a rhombus (since a rhombus is a type of parallelogram). So the contrapositive is true.

Answer:

Converse: False; Inverse: False; Contrapositive: True