Question

question 1 - 12
a pentagon has exactly 5 sides. prove the following conditional by proving the contrapositive. if a polygon does not have exactly 5 sides, then it is not a pentagon
contrapositive: if, then. since, the contrapositive is.
since the contrap a pentagon has 5 sides original statement is.
options: a pentagon has 5 sides, a polygon is a pentagon, the polygon has 5 sides

Explanation:

Step1: Define contrapositive

The contrapositive of "If a polygon does not have exactly 5 sides, then it is not a pentagon" is "If a polygon is a pentagon, then the polygon has 5 sides".

Step2: Check truth - value

Since by definition a pentagon has 5 sides, the contrapositive is true.

Step3: Determine original statement

Since a conditional statement and its contrapositive have the same truth - value, the original statement is true.

Answer:

Contrapositive: If a polygon is a pentagon, then the polygon has 5 sides. Since a pentagon has 5 sides, the contrapositive is true. Since the contrapositive is true, the original statement is true.