Question

question 10 of 25
if jklm is a trapezoid, which statements must be true? check all that apply.
a. jm ≅ kl
b. ∠j is congruent to ∠k
c. jk is parallel to lm
d. jk ≅ lm
e. ∠j is supplementary to ∠k
f. kl is parallel to jm

Explanation:

Step1: Recall trapezoid definition

A trapezoid is a quadrilateral with exactly one pair of parallel sides. In trapezoid $JKLM$, the parallel - sides are the bases.

Step2: Analyze option A

There is no information given to suggest that non - parallel sides $\overline{JM}$ and $\overline{KL}$ are congruent. This is only true for isosceles trapezoids. So, option A is not always true.

Step3: Analyze option B

$\angle J$ and $\angle K$ are adjacent angles along a non - parallel side. They are not congruent in a general trapezoid. So, option B is not always true.

Step4: Analyze option C

$\overline{JK}$ and $\overline{LM}$ are non - parallel sides in a general trapezoid. So, option C is not true.

Step5: Analyze option D

There is no information given to suggest that non - parallel sides $\overline{JK}$ and $\overline{LM}$ are congruent. This is only true for isosceles trapezoids. So, option D is not always true.

Step6: Analyze option E

$\angle J$ and $\angle K$ are adjacent angles along a non - parallel side. They are not supplementary in a general trapezoid. So, option E is not true.

Step7: Analyze option F

By the definition of a trapezoid, in trapezoid $JKLM$, one pair of opposite sides must be parallel. Here, $\overline{KL}$ is parallel to $\overline{JM}$. So, option F is true.

Answer:

F. $\overline{KL}$ is parallel to $\overline{JM}$