Question

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.

Answer 1

Statement

Reason
I

Segment DE is half the length of segment AC.

By substitution
II

Segment DE is parallel to segment AC.

Slopes of parallel lines are equal.
III

The coordinates of point D are (4, 5) and coordinates of point E are (5, 3)

By the midpoint formula
IV

Length of segment DE is 2 multiplied by the square root of 5.

By the distance formula
V

Slope of segment DE is -2 and slope of segment AC is -2.

By the slope formula

Answer 2

Which is the most logical order of statements and reasons for the proof?

III, I, IV, II, V

III, V, II, IV, I

III, IV, I, II, V

I, IV, III, V, II