Question

Given : M is the midpoint of (LT) N is the midpoint of (RF) LT=RF Prove: LM=RN

Answer 1

The proof is based on the midpoint theorem which states that the segments LM and RN, being halves of segments LT and RF respectively, must be equal if LT and RF are equal.

Step-by-step explanation:

The student's question involves a geometric proof where LM and RN are the lengths to be proven equal. Given that M is the midpoint of LT and N is the midpoint of RF, and knowing that LT is equal to RF, we can infer that LM is half the length of LT and RN is half the length of RF. Since LT equals RF, it logically follows that half their lengths would also be equal, thus LM equals RN.

Here's the step-by-step explanation:

1. Since M is the midpoint of LT, we have LM = MT = LT/2.
2. Similarly, N is the midpoint of RF, so RN = NF = RF/2.
3. Given LT = RF, we substitute into our previous equations to find that LM = LT/2 and RN = RF/2 are equivalent.
4. Therefore, LM = RN, and the proof is complete.