Question

geom_test_u2b (foundations) assessment
1 multiple choice 5 points
in quadrilateral abdc, $ab \parallel cd$. which additional piece of information is needed to determine that abdc is a parallelogram?
$\overline{ab} \cong \overline{cd}$
$\overline{ac} \cong \overline{bd}$
$\overline{ab}\perp\overline{bd}$
$\overline{cd}\perp\overline{bd}$

Explanation:

A quadrilateral is a parallelogram if one pair of opposite sides is both parallel and congruent. We already know $\overline{AB} \parallel \overline{CD}$, so we need $\overline{AB} \cong \overline{CD}$ to satisfy this condition. The other options do not confirm the required properties for a parallelogram: congruent diagonals describe rectangles, and perpendicular sides describe right trapezoids, not general parallelograms.

Answer:

$\overline{AB} \cong \overline{CD}$