Question

I need some help with a Geometry proof. I'm lost...

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
Can you give me a word bank or something for a two column proof?

Answer 1

Statement - Reason
1. K is the midpoint of MJ - 1. Given
2. L is the midpoint of NJ - 2. Given
3. Angle MJK = Angle LJN - 3. Identity
4. Line segment LK is parallel to MN - 4. Triangle midsegment theorem
5. Angle JKL = Angle JMN, and Angle JLK = Angle JNMN - 5.Transversal
6. Triangle JKL is similar to Triangle JMN - 6. AAA similarity theorem
7. JM = 2JK - 7. Statement 1
8. MN=2KL - 9. Statement 7 and 6