Question

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

Answer 1

2) By definition of the midpoint point. If a point is in the middle of a segment, then the two resulting segment are equal. 
3) Obvious, the point K is on the line MJ.
6) From statement 5 and the property of fractions. 
8) SAS statement of congruent triangles (notice the two triangles share on common angle which is between the two proportional sides)
9) The two corresponding  sides are congruent. 
10) The constant of proportionality is 2. 
11) From statement 10. 

Answer 2

Answer:

1. Given
2. Definition of Midpoint
3. Segment Congruence Postulate
4. Segment Addition Postulate
5. Substitution Property of Equality
6. Division Property of Equality
7. Reflexive Property
8. SAS Similarity Theorem
9. Corresponding Parts of Similar Triangles Are Proportional
10. Substitution
11. Multiplication Property of Equality

Let me know if these answers are correct.