Question

A line contains the points k, l, m, and n. Point k is between points m and n. Point l is between points m and k. Which of the following inequalities must be true about the lengths of these segments?

a) In
b) Ik < kn
c) Ik < ml
d) mn
e) mk

Answer 1

The inequality Ik < kn must be true about the lengths of these segments.

Step-by-step explanation:

The question states that there is a line containing the points k, l, m, and n. Point k is between points m and n, and point l is between points m and k. We are asked to determine which of the following inequalities must be true about the lengths of these segments.

1. a) In: This inequality cannot be determined based on the given information, so it is not necessarily true.
2. b) Ik < kn: This inequality is true because point k is between points m and n, so the length of segment Ik is less than the length of segment kn.
3. c) Ik < ml: This inequality is not necessarily true because point l is between points m and k, so the length of segment Ik could be greater than the length of segment ml.
4. d) mn: This is not an inequality, but rather the length of the entire segment between points m and n. It does not provide information about the lengths of the other segments.
5. e) mk: This is not an inequality, but rather the length of the entire segment between points m and k. It does not provide information about the lengths of the other segments.