anonymous
  • anonymous
Use ∆ABC to answer the question that follows. Given: ∆ABC Prove: The three medians of ∆ABC intersect at a common point. When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point. Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
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
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anonymous
  • anonymous
IV, II, III, I II, IV, I, III IV, II, I, III II, IV, III, I
anonymous
  • anonymous
It won't let me post the statements and justification in a two column

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ganeshie8
  • ganeshie8
try taking a screenshot and post the pix... here you're trying to use parallelogram properties i think
anonymous
  • anonymous
I just did.
anonymous
  • anonymous
Does this work?
1 Attachment
ganeshie8
  • ganeshie8
look at \(\triangle ABH\)
anonymous
  • anonymous
Just heads up I HAVE NO CLUE what I'm doing.
ganeshie8
  • ganeshie8
FG is the midsegment , so it is parallel to BH FG || BH
anonymous
  • anonymous
ok
ganeshie8
  • ganeshie8
its okay im sure you would get enough clue by the time we finish ;p
anonymous
  • anonymous
Alright, continue.
ganeshie8
  • ganeshie8
do the same thing for another triangle, look at \(\triangle\) AHC whats the midsegment in that triangle
anonymous
  • anonymous
EB
anonymous
  • anonymous
?
anonymous
  • anonymous
No EG?
ganeshie8
  • ganeshie8
|dw:1347462588707:dw|
ganeshie8
  • ganeshie8
|dw:1347462742317:dw|
ganeshie8
  • ganeshie8
thats right, EG is the midsegment
ganeshie8
  • ganeshie8
so EG || HC
anonymous
  • anonymous
Yay
ganeshie8
  • ganeshie8
good work :) so far. so our first statement must be which one ?
anonymous
  • anonymous
2?
ganeshie8
  • ganeshie8
Perfect !
ganeshie8
  • ganeshie8
lets continue our logic from this point
anonymous
  • anonymous
There's only two that start with two.
ganeshie8
  • ganeshie8
only one of them is true
anonymous
  • anonymous
And they both have four next
ganeshie8
  • ganeshie8
we have this so far : we got two parallel sides according to midsegment theorem : FG || BH GE || HC
ganeshie8
  • ganeshie8
|dw:1347463059283:dw|
ganeshie8
  • ganeshie8
since GE || HC, BG also parallel to HC BG || HC so next statement is IV as you said
ganeshie8
  • ganeshie8
what could be the next ?
anonymous
  • anonymous
1?
ganeshie8
  • ganeshie8
|dw:1347463185726:dw|
ganeshie8
  • ganeshie8
thats one set of parallel sides
anonymous
  • anonymous
Oh so 3?
ganeshie8
  • ganeshie8
|dw:1347463228999:dw|
ganeshie8
  • ganeshie8
thats another set of parallel sides
ganeshie8
  • ganeshie8
doesnt it make that piece a parallelogram ?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
So I was right, it's 1?
ganeshie8
  • ganeshie8
yes ofcourse you're right :)
anonymous
  • anonymous
Thanks
ganeshie8
  • ganeshie8
np.. yw ! (:
anonymous
  • anonymous
D
anonymous
  • anonymous
See you later. Thanks again!
ganeshie8
  • ganeshie8
is that a smiley D or you're saying the correct sequence is D lol
ganeshie8
  • ganeshie8
the correct sequence of statements is this : II, IV, I, III
anonymous
  • anonymous
BOTH
ganeshie8
  • ganeshie8
hmm
anonymous
  • anonymous
LOL
ganeshie8
  • ganeshie8
good luck wid ur geometry proofs looks like you're at end of course. wish u best grades :) cya
anonymous
  • anonymous
YEP thanks

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