Question

problem 11: (first taught in lesson 48) select whether the statement below is the converse, inverse, or contrapositive of the following statement: if a quadrilateral is a parallelogram, then both pairs of its opposite sides are parallel. if both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. after you pick your answer press go. a. converse b. inverse c. contrapositive

Explanation:

For a conditional statement "If \(p\), then \(q\)" (\(p
ightarrow q\)):

• The converse is "If \(q\), then \(p\)" (\(q

ightarrow p\))

• The inverse is "If not \(p\), then not \(q\)" (\(

eg p
ightarrow
eg q\))

• The contrapositive is "If not \(q\), then not \(p\)" (\(

eg q
ightarrow
eg p\))

Let \(p\) be "a quadrilateral is a parallelogram" and \(q\) be "both pairs of its opposite sides are parallel". The original statement is \(p
ightarrow q\). The new statement "If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram" is \(q
ightarrow p\) (swapped \(p\) and \(q\)).

Answer:

A. converse