Question

1. (l51) is the following sentence true?

in a trapezoid, no opposite sides are parallel.
a. yes
b. no
c. maybe
d. sometimes
e. not applicable

1. (l56) is the following sentence true?

if all four sides of a quadrilateral are congruent, then it is a square.
a. yes
b. no
c. almost never
d. almost always
e. not applicable

1. (l56) a parallelogram is ______ a rectangle.

a. always
b. sometimes
c. never
d. definitely
e. none of the above

1. (l30) the diagonals of a trapezoid ______ bisect each other.

a. always
b. sometimes
c. never
d. definitely
e. none of the above

correctly classify each quadrilateral below.

1. (l52)

a. rhombus
b. parallelogram
c. rectangle
d. trapezoid
e. none of the above

Explanation:

Question 1

Step1: Recall trapezoid definition

A trapezoid (in some definitions) has at least one pair of parallel sides; in the inclusive definition, it has one pair. So "no opposite sides parallel" is false.

Step2: Evaluate options

Option B (No) is correct as the statement is false.

Step1: Recall quadrilateral types

A quadrilateral with all four sides congruent could be a rhombus (not necessarily a square, as a square also needs right angles). So the statement is false.

Step2: Evaluate options

Option B (No) is correct.

Step1: Recall parallelogram and rectangle definitions

A parallelogram has opposite sides parallel and equal. A rectangle is a parallelogram with right angles. So a parallelogram is a rectangle only when it has right angles (e.g., a non - right - angled parallelogram is not a rectangle). Thus, it is sometimes a rectangle.

Step2: Evaluate options

Option B (sometimes) is correct.

Answer:

B. No

Question 2