Question

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

1. (1.56)

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

1. (1.50) the consecutive angles of a parallelogram are ______.

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

1. (1.51) a trapezoid has ______ altitude(s).

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

1. (1.51) the ____ of an isosceles trapezoid are ____.

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

1. (1.55) the diagonals of a rectangle are ____, and the diagonals of a rhombus are

a. perpendicular; congruent
b. congruent; congruent
c. perpendicular; perpendicular
d. congruent; perpendicular
e. not congruent; not perpendicular

Explanation:

Question 8

Step 1: Recall parallelogram angle properties

In a parallelogram, consecutive angles are supplementary (their sum is \(180^\circ\)) because adjacent angles are same - side interior angles with respect to the parallel sides, and same - side interior angles are supplementary. Complementary angles sum to \(90^\circ\), which is not the case for consecutive angles in a parallelogram. Congruent means equal, but consecutive angles in a general parallelogram are not always congruent (they are congruent in a rectangle or rhombus, but not in a general parallelogram). And the statements "never congruent" and "never supplementary" are incorrect.

Step 1: Define the altitude of a trapezoid

The altitude (height) of a trapezoid is the perpendicular distance between the two parallel sides (the bases). Since the two bases are parallel, the perpendicular distance between them is constant. However, we can draw an infinite number of line segments (altitudes) that are perpendicular to both bases and have the same length.

Step 1: Recall properties of isosceles trapezoid

• For option A: The bases of an isosceles trapezoid are parallel (by the definition of a trapezoid, it has a pair of parallel sides called bases).
• For option B: The legs of an isosceles trapezoid are not parallel (if they were parallel, it would be a parallelogram, not just a trapezoid).
• For option C: The bases of an isosceles trapezoid are not congruent (the legs are congruent, and the bases are parallel but of different lengths in a non - rectangular isosceles trapezoid).
• For option D: The diagonals of an isosceles trapezoid are congruent, not bisected (bisected diagonals are a property of parallelograms).
• For option E: The diagonals of a trapezoid are not parallel.

So the correct property is that the bases of an isosceles trapezoid are parallel.

Answer:

B. supplementary

Question 9