triangles introduction to the triangle midsegment theorem try again your answer is incorrect. - lz: your answer is incorrect. in the figure below, points j, k, and l are the midpoints of the sides of △xyz. suppose jk = 38, xz = 96, and yx = 56. find the following lengths. kl = 28 yz = 76 lz = 48

Question

Accepted Answer

# Answer:
For $ KL $: 28, $ YZ $: 76, $ LZ $: 28
# Explanation:
## Step1: Recall the Midsegment Theorem
The midsegment of a triangle is parallel to the third side and half as long. Also, the midpoints divide the sides into two equal parts.
## Step2: Find $ KL $
Since $ J, K, L $ are midpoints, $ KL $ is a midsegment parallel to $ YX $. By the midsegment theorem, $ KL=\frac{1}{2}YX $. Given $ YX = 56 $, so $ KL=\frac{56}{2}=28 $.
## Step3: Find $ YZ $
$ JK $ is a midsegment parallel to $ YZ $. By the midsegment theorem, $ JK=\frac{1}{2}YZ $. Given $ JK = 38 $, so $ YZ = 2\times JK=2\times38 = 76 $.
## Step4: Find $ LZ $
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QUESTION IMAGE

Question

Explanation:

Step1: Recall the Midsegment Theorem

Step2: Find \( KL \)

Step3: Find \( YZ \)

Step4: Find \( LZ \)

Answer: