Question

problem 12:
(first taught in lesson 48)
read the true statement below and then tell whether the converse, inverse, and contrapositive are also true.
if a polygon has four sides, then it is a quadrilateral.
converse
inverse
contrapositive
if a polygon is a quadrilateral, then it has four sides.
true
false
go

Explanation:

Step1: Define the converse, inverse, and contrapositive

• Converse: If \( q \), then \( p \). Here, \( p = \) "a polygon has four sides", \( q = \) "it is a quadrilateral". The converse is "If a polygon is a quadrilateral, then it has four sides".
• Inverse: If not \( p \), then not \( q \). The inverse is "If a polygon does not have four sides, then it is not a quadrilateral".
• Contrapositive: If not \( q \), then not \( p \). The contrapositive is "If a polygon is not a quadrilateral, then it does not have four sides".

Step2: Analyze the truth - value of each statement

• Converse: By the definition of a quadrilateral (a four - sided polygon), if a polygon is a quadrilateral, it must have four sides. So the converse is True.
• Inverse: A polygon that is not four - sided (e.g., a triangle) is not a quadrilateral. So the inverse is True.
• Contrapositive: If a polygon is not a quadrilateral (e.g., a pentagon), it does not have four sides. So the contrapositive is True.

Answer:

Converse: True; Inverse: True; Contrapositive: True