Question

for each of the following quadrilaterals, select all the properties that must be true. (a) trapezoid (b) rectangle (c) parallelogram all sides congruent four right angles only one pair of parallel sides two pairs of parallel sides

Explanation:

Step1: Recall trapezoid properties

A trapezoid has only one pair of parallel sides. It does not have all - sides congruent, four right - angles, or two pairs of parallel sides.

Step2: Recall rectangle properties

A rectangle has four right - angles and two pairs of parallel sides. It does not have all sides congruent (a square is a special case of a rectangle where all sides are congruent, but generally a rectangle doesn't have this property) and it doesn't have only one pair of parallel sides.

Step3: Recall parallelogram properties

A parallelogram has two pairs of parallel sides. It does not have all sides congruent (a rhombus is a special case of a parallelogram where all sides are congruent), four right - angles (a rectangle is a special case of a parallelogram with four right - angles), or only one pair of parallel sides.

Answer:

(a) Trapezoid: Only one pair of parallel sides
(b) Rectangle: Four right angles, Two pairs of parallel sides
(c) Parallelogram: Two pairs of parallel sides