Question

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

all sides congruent

four right angles

two pairs of parallel sides

only one pair of parallel sides

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(a) parallelogram

$square$

$square$

$square$

$square$

(b) square

$square$

$square$

$square$

$square$

(c) trapezoid

$square$

$square$

$square$

$square$

Explanation:

• Parallelogram: Defined as a quadrilateral with two pairs of parallel sides; it does not require all sides congruent or four right angles, and it has two pairs of parallel sides (not just one).
• Square: A special quadrilateral that has all sides congruent, four right angles, and two pairs of parallel sides; it cannot have only one pair of parallel sides.
• Trapezoid: Defined as a quadrilateral with exactly one pair of parallel sides; it does not require all sides congruent or four right angles, and it does not have two pairs of parallel sides.

Answer:

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

In table form (checked boxes correspond to the selected properties):

	All sides congruent	Four right angles	Two pairs of parallel sides	Only one pair of parallel sides
(b) Square	✅	✅	✅
(c) Trapezoid				✅