Please help me understand! Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
A two column proof of the theorem is shown, but a justification is missing.

Question

Please help me understand! Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
A two column proof of the theorem is shown, but a justification is missing.

anonymous · Answer

attachment

anonymous · Answer

Statement	Justification
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3)	Midpoint Formula
Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5.	
Segment DE is half the length of segment AC.	Substitution Property of Equality
Slope of segment DE is −2 and slope of segment AC is −2.	Slope Formula
Segment DE is parallel to segment AC.	Slopes of parallel lines are equal.

anonymous · Answer

What is the missing Justification?

anonymous · Answer

Additive Identity 
Distance Formula
Midsegment Theorem
Transitive Property of Equality

anonymous · Answer

you ever find the answer? i think it is midsegment theorem