Question

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Statements and reasons

I. Segment DE is parallel to segment AC.
Slopes of parallel lines are equal.

II. The coordinates of point D are (4, 5) and coordinates of point E are (5, 3).
 By the midpoint formula

III. Slope of segment DE is -2 and slope of segment AC is -2.
By the slope formula

IV. Length of segment DE is radical 5 and length of segment AC is 2 radical 5
By the distance formula

V. Segment DE is half the length of segment AC.