Question

If JKLM is a trapezoid, which statements must be true? Check all that apply.

A. KL is parallel to JM.
B. JM = KL.
C. LJ is supplementary to 2K.
D. JK is parallel to LM.
E. 2J is congruent to 4K.

Answer 1

In a trapezoid, KL is parallel to JM and JK is parallel to LM. The lengths of JM and KL do not have to be equal, and the angles are not necessarily congruent or supplementary.

Step-by-step explanation:

To determine which statements must be true for the trapezoid JKLM, we need to understand the properties of trapezoids.

A. KL is parallel to JM: This statement must be true because in a trapezoid, the pair of opposite sides are parallel, so KL must be parallel to JM.

B. JM = KL: This statement does not have to be true. The length of JM and KL can be different in a trapezoid.

C. LJ is supplementary to 2K: This statement does not have to be true. In a trapezoid, the interior angles are not necessarily supplementary.

D. JK is parallel to LM: This statement must be true because in a trapezoid, the pair of non-parallel sides are not parallel to each other.

E. 2J is congruent to 4K: This statement does not have to be true. The angles in a trapezoid are not necessarily congruent to each other.