Final answer:
To show that KL is congruent to LM, we use the fact that K and M are midpoints of JL and LN, respectively. JL is congruent to LN, so by the Transitive Property and Segment Addition Postulate, KL and LM are congruent.
Step-by-step explanation:
To prove that KL is congruent to LM, we must use the information that K is the midpoint of JL and M is the midpoint of LN. Being midpoints implies that each point divides the segment into two congruent parts. Therefore, JK is congruent to KL and LN is congruent to NM.
We can set up the congruency statement like this:
- JK ≅ KL (Midpoint Definition)
- LN ≅ NM (Midpoint Definition)
However, we also know that JL is congruent to LN because K and M are midpoints. So by the Transitive Property of congruence, which states that if two segments are congruent to the same segment, then they're congruent to each other, we can deduct the following:
- JL ≅ LN (Both double their respective midsegments)
- JK + KL ≅ LM + MN (Segment Addition Postulate)
- KL ≅ LM (Additive Property of Equality)
Therefore, segment KL is congruent to segment LM.