Provide reasons for the proof of the triangle proportionality theorem

1. KL || MN  given

2. angle JKL cog angle JMN and angle JLK cong JNM    These are corresponding angles on a traversal of parallel lines.

3. Triangle JKL similar to triangle JMN     angle angle similarlity

4. JM/JK = JN/JL     Proportionality of corresponding parts of similar triangles

5. JM=JK+KM and JN=JL+LN  Collinear segment addition postulate

6. (JK+KM)/JK = (JL+LN)/JL    Substitution

7.  ... addition of fractinos

8. ... simplify

9.  KM/JK = LN/JL        Simplify (or Subtraction something)

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