Question

Determine if KLMN must be a parallelogram. Justify your answer.

Answer 1

Answer:

(D)

Step-by-step explanation:

For there too be a parallelogram, you must have two pairs of opposite side parallel lines. This means that KN & LN must be parallel, and KL & NM have to be parallel.

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Answer 2

Answer:

Choice C

One pair of opposite sides are parallel (KN and LM). That same pair of opposite sides are also congruent. Therefore, the figure is a parallelogram.

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The tick marks tell us that the sides are congruent. So KN = LM. In short, they are the same length.

They are also parallel because of the similar arrow markers that are in the middle of the segment. If the arrows were at the endpoint of the segment, then you would have a ray. But being in the middle of the segment means "this line is parallel to any other line with the same arrow marker in the same basic position".

With this set of info, we can draw in line KM and show that angle NKM = angle LMK (alternate interior angles). Then by SAS, we can show that triangle NKM = triangle LMK. Finally, using CPCTC, we can show that KL = NM and that angle KMN = angle MKL

The fact that angles KMN and MKL are alternate interior angles would help us prove that KL and MN are parallel.

So in short, we have enough info to prove the figure is a parallelogram. Even though at first glance, it may seem that this figure is not a parallelogram (since only one pair of opposite sides are parallel).