Question

In 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.
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

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

Answer 1

The most logical order is:
- The coordinates of point D and E by the midpoint formula.
- Slope of segment DE and slope of segment AC.
- Segment DE is parallel to segment AC. Slopes of parallel lines are equal.
- Length of segment DE and length of segment AC by the distance formula.
- Segment DE is half the length of segment AC by the substitution.
Answer: B ) III, V, II, IV, I.