Question

problem 12: (lesson 48) select whether the statement below is the converse, inverse, or contrapositive of the following statement: if a quadrilateral is a parallelogram, then pairs of its consecutive angles are supplementary. if pairs of its consecutive angles are not supplementary, then a quadrilateral is not a parallelogram. after you pick your answer press go. a. converse b. inverse c. contrapositive

Explanation:

Step1: Recall the definitions

Let the original statement be “If \(p\), then \(q\)” (\(p
ightarrow q\)).

• Converse: “If \(q\), then \(p\)” (\(q

ightarrow p\))

• Inverse: “If not \(p\), then not \(q\)” (\(

eg p
ightarrow
eg q\))

• Contrapositive: “If not \(q\), then not \(p\)” (\(

eg q
ightarrow
eg p\))

Let \(p\): “A quadrilateral is a parallelogram” and \(q\): “Pairs of its consecutive angles are supplementary”

The original statement is \(p
ightarrow q\)

The given statement is “If pairs of its consecutive angles are not supplementary (\(
eg q\)), then a quadrilateral is not a parallelogram (\(
eg p\))” which is \(
eg q
ightarrow
eg p\)

Answer:

C. contrapositive