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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!!

KennedyPape  Jan 24, 2018
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1+0 Answers

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I think they are correct!

hectictar  Jan 24, 2018

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