Question

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

all sides congruent

only one pair of parallel sides

two pairs of parallel sides

four right angles

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(a) parallelogram

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(b) square

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(c) trapezoid

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Explanation:

1. Parallelogram: By definition, it has two pairs of parallel sides. It does not require all sides to be congruent (that's a rhombus), only one pair of parallel sides (that's a trapezoid), or four right angles (that's a rectangle).
2. Square: A square is a special case of parallelogram, rhombus, and rectangle. It has all sides congruent, two pairs of parallel sides, and four right angles. It does not have only one pair of parallel sides.
3. Trapezoid: The standard definition is a quadrilateral with exactly one pair of parallel sides. It does not require all sides congruent, two pairs of parallel sides, or four right angles.

Answer:

	All sides congruent	Only one pair of parallel sides	Two pairs of parallel sides	Four right angles
(b) Square	$\boxtimes$	$\square$	$\boxtimes$	$\boxtimes$
(c) Trapezoid	$\square$	$\boxtimes$	$\square$	$\square$

(Note: $\boxtimes$ indicates the checked properties)