Question

Provide a two-column proof: Given: Line segment PR is congruent to line segment LN

Q is the midpoint of line segment PR
M is the midpoint of line segment LN
Prove: PQ = LM

Answer 1

To prove that PQ = LM, we can use the concept of congruent triangles. By showing that triangle PQR is congruent to LNM, we can establish that their corresponding sides are congruent, proving that PQ = LM.

Step-by-step explanation:

We are given that line segment PR is congruent to line segment LN and that Q is the midpoint of line segment PR and M is the midpoint of line segment LN. We need to prove that PQ = LM.

To prove this, we can use the concept of congruent triangles. Since PR is congruent to LN, we can say that triangle PQR is congruent to triangle LNM by the Side-Side-Side (SSS) congruence theorem.

Since PQR is congruent to LNM, their corresponding sides are congruent. Therefore, PQ is congruent to LM, which proves that PQ = LM.

Answer 2

1) Line segment PR is congruent to line segment LN, Q is the midpoint of line segment PR, M is the midpoint of line segment LN (given)

2) PQ=PR, LM=LN (a midpoint splits a segment into two congruent parts)

3) PQ=LM (halves of congruent segments are congruent)