Question

What is the converse of the conditional statement?

"If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid."
Responses

A. If a quadrilateral is not a trapezoid, then it does not have exactly one pair of parallel sides.
B. If a quadrilateral does not have exactly one pair of parallel sides, then it is not a trapezoid.
C. If a quadrilateral does not have exactly one pair of parallel sides, then it is a trapezoid.
D. If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides.

Answer 1

D. If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides.

Explanation:

The converse of a statement is formed by switching the hypothesis and the conclusion.

• Hypothesis: The part after the "if".
• Conclusion: The part after the "then".

Given statement:

• "If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid."

Therefore:

• Hypothesis: "a quadrilateral has exactly one pair of parallel sides"
• Conclusion: "it is a trapezoid."

Converse statement:

• "If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides."