Question

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

Explanation:

Step1: Properties of parallelogram

By definition, a parallelogram has two pairs of parallel sides. So for the property "Two pairs of parallel sides", (a) Rectangle (since a rectangle is a type of parallelogram), (b) Parallelogram, (c) Rhombus (since a rhombus is a type of parallelogram) should be selected.

Step2: Properties of quadrilaterals with only one pair of parallel sides

A rectangle, parallelogram, and rhombus are all parallelograms (with two pairs of parallel sides). So for the property "Only one pair of parallel sides", none of (a), (b), (c) should be selected.

Step3: Properties of having four right - angles

A rectangle has four right - angles. A parallelogram (in general) does not have four right - angles (unless it is a rectangle), and a rhombus (in general) does not have four right - angles (unless it is a square, which is a special case of a rhombus and a rectangle). So for the property "Four right angles", only (a) Rectangle should be selected.

Step4: Properties of having all sides congruent

A rhombus has all sides congruent. A rectangle (in general) has opposite sides congruent, and a parallelogram (in general) has opposite sides congruent. So for the property "All sides congruent", only (c) Rhombus should be selected.

Answer:

• Two pairs of parallel sides: (a) Rectangle, (b) Parallelogram, (c) Rhombus
• Only one pair of parallel sides: None of (a), (b), (c)
• Four right angles: (a) Rectangle
• All sides congruent: (c) Rhombus