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

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

Answer 2

III, I, IV, II, V

III, V, II, IV, I

III, IV, I, II, V

I, IV, III, V, II

Answer 3

@phi

Answer 4

some statements must come before others.
can you find any statements where the order matters?

Answer 5

i think its the third one, but im not positive! @phi

Answer 6

Look at statement II and statement V
one should go first, because the other one depends on knowing the first one.
what order do you think they should be in ?

Answer 7

2nd one i get it thanks! @phi

Answer 8

which comes first II or V?

Answer 9

II

Answer 10

II Segment DE is parallel to segment AC.
Slopes of parallel lines are equal.

II says DE is parallel to AC because the slopes are equal

How do you know the slopes are equal?

Look at V


V Slope of segment DE is -2 and slope of segment AC is -2.
By the slope formula

V says the slopes are equal (by using the slope formula)

so what order makes sense?

Answer 11

the first one!

Answer 12

Think like this:
Slopes equal means DE is parallel to AC
so you need to first show slopes are equal (that is what V does)

then you use the idea that slopes are equal to prove DE is parallel to AC

so first you do V, then II

look at your choices and cross out any that have II before V in their list.

Answer 13

the second

Answer 14

@phi

Answer 15

CAN I?

Answer 16

the 1st and 3rd choices are out.
that leaves 2nd or 4th.

Answer 17

and 4th is out cause III must be the first statement

Answer 18

so it is the II

Answer 19

Look at III and IV

you see that IV uses the distance formula, so you need points

III gives you the points.
so what order should III and IV be in?

Answer 20

YEP

Answer 21

so what was the answer to this? I still don't get it.