Question

1. which description does not guarantee that a quadrilateral is a parallelogram? a. a quadrilateral with both pairs of opposite sides congruent b. a quadrilateral with the diagonals bisecting each other c. a quadrilateral with consecutive angles supplementary d. quadrilateral with two opposite sides parallel for quadrilateral abcd with vertices a(- rhombus

Explanation:

• Option A: A quadrilateral with both pairs of opposite sides congruent is a proven parallelogram theorem.
• Option B: A quadrilateral with diagonals bisecting each other is a core parallelogram criterion.
• Option C: Consecutive angles being supplementary only proves that one pair of sides is parallel; the other pair may not be, so this does not guarantee a parallelogram (e.g., a trapezoid with one pair of parallel sides has supplementary consecutive angles but is not a parallelogram).
• Option D: A quadrilateral with two opposite sides parallel is not the full definition, but wait—correction: actually, the key is that option C's condition applies to trapezoids as well, while the others are strict parallelogram rules. Consecutive supplementary angles only confirm one set of parallel sides, not two pairs required for a parallelogram.

Answer:

C. a quadrilateral with consecutive angles supplementary