Question

which of these figures must be a rectangle?
a. a trapezoid with two congruent sides
b. a parallelogram with at least one right angle
c. a trapezoid with at least one right angle
d. a parallelogram with four congruent sides

Explanation:

Step1: Recall trapezoid properties

A trapezoid has only one - pair of parallel sides. A trapezoid with two congruent sides (A) or at least one right - angle (C) is not necessarily a rectangle as rectangles have two pairs of parallel sides.

Step2: Recall parallelogram properties

In a parallelogram, opposite angles are congruent. If a parallelogram has at least one right - angle, then all of its angles are right - angles (since adjacent angles in a parallelogram are supplementary, and opposite angles are equal). A parallelogram with all right - angles is a rectangle.

Step3: Analyze option D

A parallelogram with four congruent sides is a rhombus, not necessarily a rectangle.

Answer:

B. A parallelogram with at least one right angle