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 Square root of 5and length of segment AC 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, V, II, IV, I

III, I, IV, II, V

III, IV, I, II, V

I, IV, III, V, II

Answer 3

that's the figure I just posted