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 the statement and reasons are not in correct order.
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Segment DE is half the length of segment AC.
Length of segment DE is and length of segment AC is .
By the distance formula
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3)
By the midpoint formula
Segment DE is parallel to segment AC.
Slopes of parallel lines are equal.
Slope of segment DE is -2 and slope of segment AC is -2.
By the slope formula
Which is the most logical order of statements and reasons for the proof?
I, IV, III, II, V
III, I, II, IV, V
I, III, II, V, IV
III, II, I, V, IV