Question

Consider the following statement. Every parallelogram is a quadrilateral.

(a) Write the converse of the given statement.
A figure is a parallelogram if and only if it is a quadrilateral.
If a figure is a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is a parallelogram.
If a figure is a quadrilateral, then it is a parallelogram.
If a figure is not a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is not a parallelogram.

(b) Write the inverse of the given statement.
A figure is a parallelogram if and only if it is a quadrilateral.
If a figure is a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is a parallelogram.
If a figure is a quadrilateral, then it is a parallelogram.
If a figure is not a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is not a parallelogram.

(c) Write the contrapositive of the given statement.
A figure is a parallelogram if and only if it is a quadrilateral.
If a figure is a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is a parallelogram.
If a figure is a quadrilateral, then it is a parallelogram.
If a figure is not a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is not a parallelogram.

Answer 1

The converse of the statement is if a figure is a parallelogram, then it is a quadrilateral. The inverse is if a figure is not a parallelogram, then it is not a quadrilateral. The contrapositive is if a figure is not a quadrilateral, then it is not a parallelogram.

Step-by-step explanation:

(a) Converse: If a figure is a parallelogram, then it is a quadrilateral.

(b) Inverse: If a figure is not a parallelogram, then it is not a quadrilateral.

(c) Contrapositive: If a figure is not a quadrilateral, then it is not a parallelogram.