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.

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).

The best answer is "D"

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

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 ".

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents