Question

Practice applying the side-splitter theorem, its converse, and the triangle midsegment theorem.

Triangle J L N is cut by line segment K M. LIne segment K M goes from side J L to side L N. The length of J K is 10, the length of K L is 16, the length of L M is 24, and the length of M N is 15.

Is KM ∥ JN? Why or why not?

No, because StartFraction 16 Over 10 EndFraction not-equals StartFraction 24 Over 15 EndFraction.
Yes, because StartFraction 10 Over 24 EndFraction equals StartFraction 15 Over 16 EndFraction.
Yes, because StartFraction 16 Over 10 EndFraction equals StartFraction 15 Over 24 EndFraction
Yes, because StartFraction 16 Over 10 EndFraction equals StartFraction 24 Over 15 EndFraction.

Answer 1

KM is not parallel to JN because the ratio of segments JK:KL is 5:8, which is not equal to the ratio of segments LM:MN, which is 8:5. They are inverse and thus not parallel.

Step-by-step explanation:

When applying the side-splitter theorem and its converse, we analyze the ratios of the lengths of segments formed when a line is drawn parallel to one side of a triangle, intersecting the other two sides.

In this case, we have a line segment KM intersecting sides JL and LN of triangle JLN and need to determine if KM is parallel to JN by comparing the ratios of the segments.

According to the side-splitter theorem, if KM were parallel to JN, the ratios of the lengths of the segments it intersects would be equal; that is, JK:KL should be equal to LM:MN. We have JK = 10, KL = 16, LM = 24, and MN = 15.

Now, we calculate the ratios. The ratio JK:KL is 10:16, which simplifies to 5:8. The ratio LM:MN is 24:15, which simplifies to 8:5. Since the ratios are the inverse of each other and not equal, KM is not parallel to JN.

The correct answer is:

• No, because 16/10 does not equal 24/15.