Provide the missing reasons for the proof of part of the triangle midsegment theorem.

Given: K is the midpoint of MJ.

L is the midpoint of NJ.

Prove: MN = 2KL

Statement: ~ Reason:

1. K is the midpoint of MJ. L is the midpoint of NJ. ~ Given

2. MK ≅ KJ and NL ≅ LJ ~ **Definition of Midpoint**

3. MK = KJ and NL = LJ ~ **Segment Congruence Postulate**

4. MJ = MK + KJ and NJ = NL + LJ ~ **Segment Addition Postulate**

5. MJ = 2KJ and NJ = 2LJ ~ Substitution Property of Equality

6. MJ/KJ = NJ/LJ = 2 ~ Division Property of Equality

7. ∠J ≅ ∠J ~ **Reflexive Property**

8. ΔJMN ~ ΔJKL ~ **SAS Similarity Theorem**

9. MN/KL = MJ/KJ ~ **Corresponding parts of similar triangles are proportional**

10. MN/KL = 2 ~ **Substitution**

11. MN = 2KL ~ **Multiplication Property of Equality**

*****All bolded words are my answers. Can you please check them, and correct me if they are wrong*****

Thank you!!

KennedyPape
Jan 24, 2018