Question

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

A triangle with vertices A(6, 8), B(2,2) and C(8, 4) and segment DE. Point D is on side AB and point E is on side BC..



Statement
Reason
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

Answer 1

IV
Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5.
By the distance formula
V
Segment DE is half the length of segment AC.
By substitution

Which is the most logical order of statements and reasons for the proof?
III, II, I, IV, V

II, III, I, IV, V

II, I, III, V, IV

III, I, IV, V, II