10
QuizMultiple Choice

Constructing Geometric Figures

Question 10 • Math 7 B (M12 25/26 S2)

Nico and Karina wrote these statements in their math journals.Nico’s StatementKarina’s StatementA 4-sided polygon with at least one pair of parallel sides must be a parallelogram.A 4-sided polygon with at least one pair of parallel sides must be a trapezoid.Which describes the accuracy of their statements and why?

Answer
A
Nico is correct because if one pair of sides in a quadrilateral is parallel, the other pair must be also.
B
Karina is correct because a trapezoid has exactly one pair of parallel sides.
C
Both are correct because a 4-sided polygon with at least one pair of parallel sides must be both a parallelogram and a trapezoid.
D
Neither is correct because a 4-sided polygon with at least one pair of parallel sides could be either a parallelogram or a trapezoid.

Explanation

A quadrilateral with at least one pair of parallel sides could have exactly one parallel pair, making it a trapezoid, or two parallel pairs, making it a parallelogram. So Nico’s statement is too broad, and Karina’s is also too broad because the quadrilateral need not have exactly one pair. Neither statement is always correct; choice D describes this distinction.

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