Question

always, sometimes, or never?
a parallelogram has right angles.

select one:
a. sometimes
b. never
c. always

always, sometimes, or never?
using the exclusive definition of a trapezoid, a square is a trapezoid.

select one:
a. always
b. never
c. sometimes

which is a distinguishing property of a rectangle?

select one:
a. all sides are equal.
b. only one pair of opposite sides are parallel.
c. opposite angles are not equal.
d. all angles are 90 degrees.

always, sometimes, or never?
the diagonals of a rectangle are congruent.

Explanation:

Analyze the first question

A parallelogram is a quadrilateral with two pairs of parallel opposite sides. If a parallelogram has one right angle, all of its angles must be right angles, making it a rectangle. Since some parallelograms are rectangles and others are not, a parallelogram has right angles sometimes.

Analyze the second question

The exclusive definition of a trapezoid states that it is a quadrilateral with exactly one pair of parallel sides. A square has two pairs of parallel sides. Under the exclusive definition, a square can never be a trapezoid.

Analyze the third question

A rectangle is defined as a quadrilateral with four right angles. Therefore, having all angles equal to 90 degrees is its distinguishing property.

Analyze the fourth question

By the properties of rectangles, the diagonals of any rectangle are always congruent.

Answer:

Question 1

• a. Sometimes (Correct answer)
• b. Never
• c. Always

Question 2

• a. Always
• b. Never (Correct answer)
• c. Sometimes

Question 3

• a. All sides are equal.
• b. Only one pair of opposite sides are parallel.
• c. Opposite angles are not equal.
• d. All angles are 90 degrees. (Correct answer)

Question 4

• a. Always (Correct answer)
• b. Sometimes
• c. Never