Question

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

	four right angles	all sides congruent	only one pair of parallel sides	two pairs of parallel sides
(a) rectangle	$square$	$square$	$square$	$square$
(b) trapezoid	$square$	$square$	$square$	$square$
(c) parallelogram	$square$	$square$	$square$	$square$

Explanation:

For (a) Rectangle:

• Four right angles: By definition, a rectangle has four right angles (90° each). So this property is true.
• All sides congruent: A rectangle has opposite sides congruent, but not all sides (unless it's a square, a special case). So this is false.
• Only one pair of parallel sides: A rectangle has two pairs of parallel sides (opposite sides are parallel). So this is false.
• Two pairs of parallel sides: Opposite sides of a rectangle are parallel, so there are two pairs. This is true.

For (b) Trapezoid:

• Four right angles: A trapezoid (general) does not have four right angles (only a right trapezoid has two). So false.
• All sides congruent: A trapezoid does not have all sides congruent (unless it's a special isosceles trapezoid with additional properties, but not all trapezoids). So false.
• Only one pair of parallel sides: By definition, a trapezoid has exactly one pair of parallel sides (in the US definition; some definitions say at least one, but the "only one" here is the common US definition). So this is true.
• Two pairs of parallel sides: A trapezoid with two pairs of parallel sides is a parallelogram, so a general trapezoid has only one pair. So false.

For (c) Parallelogram:

• Four right angles: A parallelogram has four right angles only if it's a rectangle (a special case). So false.
• All sides congruent: A parallelogram has opposite sides congruent, but not all sides (unless it's a rhombus, a special case). So false.
• Only one pair of parallel sides: A parallelogram has two pairs of parallel sides. So false.
• Two pairs of parallel sides: By definition, a parallelogram has two pairs of parallel sides (opposite sides are parallel). So this is true.

Answer:

	Four right angles	All sides congruent	Only one pair of parallel sides	Two pairs of parallel sides
(b) Trapezoid	$\boldsymbol{\square}$	$\boldsymbol{\square}$	$\boldsymbol{\checkmark}$	$\boldsymbol{\square}$
(c) Parallelogram	$\boldsymbol{\square}$	$\boldsymbol{\square}$	$\boldsymbol{\square}$	$\boldsymbol{\checkmark}$