Question

Which statement is the inverse of the following?

"If a polygon has four sides, then it is called a quadrilateral."
A. If a quadrilateral has four sides, then it is called a polygon.
B. If a polygon is called a quadrilateral, then it has four sides.
C. If a polygon is not called a quadrilateral, then it does not have four sides.
D. If a polygon does not have four sides, then it is not called a quadrilateral.

Answer 1

The best answer is "D"

If a polygon does not have four sides, then it is not called a quadrilateral.

Step-by-step explanation:

If P ⇒ Q is a statement, then the inverse of this statement is:

not Q ⇒ not P.

A statement and its inverse are equivalent.

For the statement :

"If a polygon has four sides, then it is called a quadrilateral."

The inverse is " If a polygon does not have four sides, then it is not called a quadrilateral ".

Answer 2

C. If a polygon is not called a quadrilateral, then it does not have four sides.

Step-by-step explanation:

If P ⇒ Q is a statement, then the contra positive of this statement is:

not Q ⇒ not P.

A statement and its contra positive are equivalent.

The given statement is :

"If a polygon has four sides, then it is called a quadrilateral."

The contra positive of the above is:

"If a polygon is not called a quadrilateral, then it does not have four sides" which is given in (C).

Hence, the correct option is (C).