Question

1. (l51)

a. isosceles trapezoid
b. trapezoid
c. rhombus
d. square
e. rectangle

1. (l56)

a. rectangle
b. isosceles trapezoid
c. trapezoid
d. rhombus
e. parallelogram

1. (l50) the consecutive angles of a parallelogram are ______.

a. complementary
b. supplementary
c. congruent
d. never congruent
e. never supplementary

1. (l51) a trapezoid has ______ altitude(s).

a. one
b. two
c. four
d. an infinite number of
e. zero

1. (l51) the ____ of an isosceles trapezoid are ____.

a. bases; parallel
b. legs, parallel
c. bases; congruent
d. diagonals; bisected
e. diagonals; parallel

the diagonals of a rectangle are ______, and the diagonals of

Explanation:

Question 6

Step1: Analyze the figure

The figure has four right angles (marked by the square corners) and opposite sides appear equal and parallel.

Step2: Recall definitions

• Isosceles trapezoid: A trapezoid with congruent legs, not all angles right.
• Trapezoid: A quadrilateral with at least one pair of parallel sides, not all angles right.
• Rhombus: A parallelogram with all sides equal, angles not necessarily right.
• Square: A rectangle with all sides equal (this figure doesn't show all sides equal, just right angles and opposite sides equal).
• Rectangle: A parallelogram with four right angles. The figure matches this.

Step1: Analyze the figure

The figure has two right angles, one pair of parallel sides (marked by arrows), and the other two sides are not parallel (one is slanted).

Step2: Recall definitions

• Rectangle: Four right angles, both pairs parallel (this figure has only one pair parallel with two right angles, not four).
• Isosceles trapezoid: Legs are congruent, this figure's non - parallel sides (legs) are not congruent (one is vertical, one is slanted).
• Trapezoid: A quadrilateral with at least one pair of parallel sides. This figure has one pair of parallel sides (marked by arrows) and is a trapezoid.
• Rhombus: All sides equal, parallel sides, angles not right (doesn't match).
• Parallelogram: Both pairs of opposite sides parallel (this figure has only one pair parallel).

Step1: Recall parallelogram properties

In a parallelogram, consecutive angles are supplementary. This is because \(AB\parallel CD\) and \(AD\) is a transversal, so \(\angle A+\angle D = 180^{\circ}\) (same - side interior angles are supplementary), and similarly for other consecutive angles.

Step2: Analyze options

• Complementary: Sum to \(90^{\circ}\), not true for consecutive angles in parallelogram.
• Supplementary: Sum to \(180^{\circ}\), which is true.
• Congruent: Consecutive angles are not always congruent (except in rectangles, but the question is about general parallelogram).
• Never congruent: In rectangles (a type of parallelogram) consecutive angles are congruent (all \(90^{\circ}\)), so this is false.
• Never supplementary: False, as we know they are supplementary.

Answer:

E. rectangle

Question 7