Question

question 13 of 25
in the diagram below, kl = 12 and lm = 8. which additional facts would guarantee that jklm is a parallelogram? check all that apply.
□ a. jk = 8, and (overline{jk}) is parallel to (overline{lm}).
□ b. jk = 12, and (overline{jm}) is parallel to (overline{kl}).
□ c. jk = 8, jm = 8
□ d. jk = 8, jm = 12

Explanation:

Step1: Recall parallelogram properties

A parallelogram has opposite - sides equal and parallel. In quadrilateral $JKLM$, we know $KL = 12$ and $LM = 8$.

Step2: Analyze option A

If $JK = 8$ and $\overline{JK}$ is parallel to $\overline{LM}$, then one pair of opposite - sides is equal and parallel, which guarantees $JKLM$ is a parallelogram.

Step3: Analyze option B

If $JK = 12$ and $\overline{JM}$ is parallel to $\overline{KL}$, this does not guarantee a parallelogram as the side - length relationships are not in line with the opposite - sides equal property.

Step4: Analyze option C

If $JK = 8$ and $JM = 8$, this does not guarantee a parallelogram as it does not satisfy the property of opposite - sides being equal and parallel in the correct way.

Step5: Analyze option D

If $JK = 8$ and $JM = 12$, then $JK = LM = 8$ and $JM = KL = 12$, which means opposite - sides are equal, guaranteeing $JKLM$ is a parallelogram.

Answer:

A. $JK = 8$, and $\overline{JK}$ is parallel to $\overline{LM}$; D. $JK = 8$, $JM = 12$