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
IV

Answer 1

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

Answer 2

What exactly are you asking?

Answer 3

Sorry, I didn't mention that lol, I'm new at this. I'm asking in what order should they go in

Answer 4

Okay, that's what I was thinking. A mathematical reasoning usually have statements which builds upon one another, so see if you can connect the reason of one statement to another statement. For example, III comes before I, since III shows that the slopes are the same by direct calculation and I uses this to deduce that DE and AC is parallell.

Answer 5

I'll give another link to help you out, II -> IV, since in II the coordinates of D and E calculated, and in IV this is used to calculate the length of DE (by the distance formula).