Question

If a polygon is a regular pentagon, then it has 5 sides.

State the converse of the conditional statement and determine whether it is true or false

Answer 1

If a polygon has 5 sides, then it is a regular pentagon
False: regular pentagon = equiangular.  There are pentagons that have 5 sides that are not equiangular

Answer 2

Answer:  The converse is "If a polygon has 5 sides, then it is a regular pentagon" and it is FALSE.

Step-by-step explanation:  We are given to state the converse of the following conditional statement and to determine whether it is true or false :

"If a polygon is a regular pentagon, then it has 5 sides".

We know that

the converse of a conditional statement "p ⇒ q" is given by "q ⇒ p".

Therefore, the CONVERSE of given conditional statement is

"If a polygon has 5 sides, then it is a regular pentagon".

The converse is not true, because if a polygon has 5 sides, then it is a pentagon, not necessarily a regular pentagon.

Thus, the converse is "If a polygon has 5 sides, then it is a regular pentagon" and it is FALSE.