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Statements
Justifications
Point F is a midpoint of Line segment AB
Point E is a midpoint of Line segment AC
Draw Line segment BE
Draw Line segment FC
by Construction
Point G is the point of intersection between Line segment BE and Line segment FC
Intersecting Lines Postulate
Draw Line segment AG
by Construction
Point D is the point of intersection between Line segment AG and Line segment BC
Intersecting Lines Postulate
Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH
by Construction
I
BGCH is a parallelogram
Properties of a Parallelogram (opposite sides are parallel)
II
Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC
Midsegment Theorem
III
Line segment BD ≅ Line segment DC
Properties of a Parallelogram (diagonals bisect each other)
IV
Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC
Substitution
Line segment AD is a median
Definition of a Median

IV, II, III, I
II, IV, I, III
IV, II, I, III
II, IV, III, I

It won't let me post the statements and justification in a two column

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I just did.

Does this work?

look at \(\triangle ABH\)

Just heads up I HAVE NO CLUE what I'm doing.

FG is the midsegment , so it is parallel to BH
FG || BH

ok

its okay im sure you would get enough clue by the time we finish ;p

Alright, continue.

EB

No EG?

|dw:1347462588707:dw|

|dw:1347462742317:dw|

thats right, EG is the midsegment

so EG || HC

Yay

good work :) so far.
so our first statement must be which one ?

2?

Perfect !

lets continue our logic from this point

There's only two that start with two.

only one of them is true

And they both have four next

we have this so far :
we got two parallel sides according to midsegment theorem :
FG || BH
GE || HC

|dw:1347463059283:dw|

since GE || HC,
BG also parallel to HC
BG || HC
so next statement is IV as you said

what could be the next ?

1?

|dw:1347463185726:dw|

thats one set of parallel sides

Oh so 3?

|dw:1347463228999:dw|

thats another set of parallel sides

doesnt it make that piece a parallelogram ?

Yes

So I was right, it's 1?

yes ofcourse you're right :)

Thanks

np.. yw ! (:

See you later. Thanks again!

is that a smiley D or you're saying the correct sequence is D lol

the correct sequence of statements is this :
II, IV, I, III

BOTH

hmm

LOL

good luck wid ur geometry proofs looks like you're at end of course. wish u best grades :) cya

YEP thanks

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