Question

is each biconditional statement true or false? select true or false for each statement. a polygon is a square if and only if the polygon has exactly four sides. a polygon has exactly five sides if and only if the polygon is a pentagon. a polygon has exactly four sides if and only if the polygon is a rectangle.

Explanation:

Step1: Analyze first statement

A square has four - equal sides and four right - angles. Just having four sides doesn't make a polygon a square. So "A polygon is a square if and only if the polygon has exactly four sides" is false.

Step2: Analyze second statement

By definition, a pentagon is a polygon with five sides and a polygon with five sides is a pentagon. So "A polygon has exactly five sides if and only if the polygon is a pentagon" is true.

Step3: Analyze third statement

A rectangle has four sides, but a polygon with four sides isn't necessarily a rectangle (it could be a trapezoid etc.). So "A polygon has exactly four sides if and only if the polygon is a rectangle" is false.

Answer:

A polygon is a square if and only if the polygon has exactly four sides: False
A polygon has exactly five sides if and only if the polygon is a pentagon: True
A polygon has exactly four sides if and only if the polygon is a rectangle: False