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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!!
