+8 Hello! Thanks in advance!
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 as a sum.
8. 1 + KM/JK = 1 + LN/JL
8. Simplify.
9. KM/JK = LN/JL
9.
+128474 1. Line segment KL is parallel to segment MN
1. Given
2. Angle JKL = Angle JMN ; Angle JLK = Angle JLK = Angle JNM
2. Parallel lines cut by a transversal make corresponding angles equal
3. Triangle JKL is similar to Triangle JMN
3. AA congruency
4. JM / JK = JN /JL
4. Correspnding sides of similar triangles are proportional to each other
5. JM = JK + KM and JN = JL + LN
5. Segment addition Postulate
6. JK + KM/ JK = JL + LN/JL
6. Substitution of (5) into (4)
7. JK/JK + KM/JK = JL/JL + LN/JL
7. Rewrite as a sum.
8. 1 + KM/JK = 1 + LN/JL
8. Simplify.
9. KM/JK = LN/JL
9. Equality Property of Subtraction
