Question

for each of the following quadrilaterals, select all the properties that must be true.

(a) parallelogram

(b) square

(c) trapezoid

Explanation:

• Parallelogram: By definition, a parallelogram has two pairs of parallel sides. It does not necessarily have four right angles or all sides congruent, and it has more than one pair of parallel sides (so not "only one pair").
• Square: A square is a special parallelogram. It has two pairs of parallel sides (as a parallelogram), four right angles (as a rectangle), and all sides congruent (as a rhombus).
• Trapezoid: By definition, a trapezoid has only one pair of parallel sides. It does not have two pairs of parallel sides (unless it's a parallelogram, but trapezoid definition in standard cases is one - pair), and it does not necessarily have four right angles or all sides congruent.

Answer:

• (a) Parallelogram: Two pairs of parallel sides.
• (b) Square: Two pairs of parallel sides, Four right angles, All sides congruent.
• (c) Trapezoid: Only one pair of parallel sides.