Provide reasons for the proof of the triangle proportionality theorem. Given: Line segment KL Prove: KM/JK = LN/JL Statement Reason 1. Line segment...

2.Provide reasons for the proof of the triangle proportionality theorem.

Given: Line segment KL

Prove: KM/JK = LN/JL

Statement

Reason

1. Line segment KL box line segment MN

1. Given

2.

2.

3. box JKL two boxes JMN

3.

4. JM/JK = JN/JL

4.

5. JM = JK + KM and JN = JL + LN

5.

6. JK + KM/ JK = JL + LN/JL

6.

7. JK/JK + KM/JK = JL/JL + LN/JL

7. Rewrite s a sum.

8. 1 + KM/JK = 1 + LN/JL

8. Simplify.

9. KM/JK = LN/JL

9.