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Help With a Math Problem Geometry

http://i.imgur.com/TdzRJ.png
I need to use a 2 column proof, and I suck with that stuff. 2 column proof like one side is statement, other is reason. Example starting this proof is LEFT SIDE : 1)Angle M is congruent to angle N, angle OKL is congruent to ANGLE OLK. RIGHT SIDE : 1)Given, and so on.
@DrHye

October 29, 2012

17 Comments • Newest first

radkai

@alex3650: Understandable. But one thing you should know is the intuition behind all the math you learn. Once you get the intuition it's all a breeze, trust me.

Reply October 29, 2012
alex3650

[quote=radkai]@alex3650: No problem. Grade actually has nothing to do with this. When I was freshman I was way sharper in geometry than now (senior).[/quote]
I prefer algebra over geo. , since I was mostly taught of using formulas, plugging in numbers, etc, it was way easier xP

Reply October 29, 2012
radkai

@alex3650: No problem. Grade actually has nothing to do with this. When I was freshman I was way sharper in geometry than now (senior).

I remember doing 16 steps in 3D geometry with planes and stuff.

Reply October 29, 2012 - edited
alex3650

[quote=radkai]1 Angle M congruent Angle N angle OKL congruent angle OLK 1 Given
2 segment OK congruent segment OL 2 sides opposite congruent angles in a triangle are congruent
3 angle MOK congruent angle NOL 3 vertical angles are congruent
4 triangle MOK congruent triangle NOL 4 AAS Theorem
5 segment MO congruent segment NO 5 corresponding sides of congruent triangles are congruent

If you struggle with 5 steps proof, what's going to happen when you get to 16 steps...[/quote]
Thanks (Freshmen here), when do we get to learn about 16 steps?

Reply October 29, 2012 - edited
radkai

1 Angle M congruent Angle N angle OKL congruent angle OLK 1 Given
2 segment OK congruent segment OL 2 sides opposite congruent angles in a triangle are congruent
3 angle MOK congruent angle NOL 3 vertical angles are congruent
4 triangle MOK congruent triangle NOL 4 AAS Theorem
5 segment MO congruent segment NO 5 corresponding sides of congruent triangles are congruent

If you struggle with 5 steps proof, what's going to happen when you get to 16 steps...

@ayashiboi What a fatal assumption you made when you said ML = NK with no proof.

Reply October 29, 2012 - edited
alex3650

[quote=looooooool]Angle-Angle-Side Postulate (AAS)

Angle M = Angle N
Angle OKL = Angle OLK
Side KL = Side LK

Therefore triangles MKL and NKL are congruent.
And so segment NO = segment MO. (Not sure if this last step has a required postulate/theorem but it seems pretty intuitive).[/quote]

I needa explain how I got it for the reason part of the column, if I ever state anything such as blah blah blah is blah blah blah, because it is given or because of vertical angles theorem, or something/etc.
@FiendOverlord Thanks, i'll try to see all of the info. that everyone has given me and make it into my final answer.

Reply October 29, 2012 - edited
FiendOverlord

-Triangle OKL isosceles by defintion(or isosceles triangle theorem i think)
-OK=OL by definition of isosceles
-Angle NOL and Angle KOM are congruent by vertical angles theorem
-Triangles MOK and NOL are congruent by AAS theorem err postulate...
-MO=NO are congruent by corresponding sides.

EDIT: I put angle instead of the segments. My bad

Reply October 29, 2012 - edited
ayashiboi

okay i don't know my geometry theorems, but MO is congruent to NO. this might be TOTALLY WRONG (probably is) but maybe this can help you somehow?
note: '<' = angle, and '_' = line segment

so <OKL congruent to <OLK => that means _OK == _OL (since it's an isosceles triangle), and _KL is that other, unequal line
now, since <M congruent to <N => that means _ML == _NK (since they have that common _KL)

now our general forumlas that we're looking at is _ML - _OL = _MO, and _NK - _OK = _NO
since _OK == _OL and _ML == _NK, we can replace one formula with the other equivalent, so...

_ML - _OL = _MO
(replace _ML with _NK since they're equal)
_NK - _OL = _MO
(replace _OL with _OK, since they're equal)
_NK - _OK = _MO
(and now since _NK - OK = _NO, we replace that...)
_NO = _MO // end of proof

remember this has no use of any theorems so it's probably wrong, but it might help you with your approach?

Reply October 29, 2012 - edited
alex3650

[quote=QinShihuangdi]@iMetricZero
In Geometry, it does not matter how the picture looks. You CANNOT make assumptions, even if it looks somewhat off

Sorry, I can't help you right now, I'm too tired.[/quote]
Awhs

@flamedagger Doesn't really matter how I drew it, I just drew the shape that was shown for the problem, the given stuff were not added into the diagram.

Reply October 29, 2012 - edited
QinShihuangdi

@iMetricZero
In Geometry, it does not matter how the picture looks. You CANNOT make assumptions, even if it looks somewhat off

Sorry, I can't help you right now, I'm too tired.

Reply October 29, 2012 - edited
flamedagger

it might help if you draw your diagram better...those angles are definitely not congruent.

Reply October 29, 2012 - edited
alex3650

[quote=DrHye]Uh, I'm guessing you're right around the lessons with all those side-angle-side and whatnot theorems, and I feel those may be relevant

Honestly I'm not too fluent with geometry theorems since they're not used too often (if I tutor a geometry class I just re-learn it five minutes earlier) so sorry [/quote]
Haha, right on . I dislike the ASA, SSS, etc theorems and postulates . T n T

Reply October 29, 2012 - edited
DrHye

Uh, I'm guessing you're right around the lessons with all those side-angle-side and whatnot theorems, and I feel those may be relevant

Honestly I'm not too fluent with geometry theorems since they're not used too often (if I tutor a geometry class I just re-learn it five minutes earlier) so sorry

Reply October 29, 2012 - edited
alex3650

[quote=TheHazza]so easy...[/quote]
Help please, i'm terrible with 2 column proofs, most of the time when I do these, I do it half way or finish the statement (left side) part, but not the reason side(right).
[quote=pieshadowxx]Def of mid point or something like that.[/quote]
Can't use midpoint.

Reply October 29, 2012 - edited
pieshadowxx

Def of mid point or something like that.

Reply October 29, 2012 - edited
TheHazza

so easy...

Reply October 29, 2012 - edited