Can anybody get this Geo Quiz,

Hint:

You need to add some lines.

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- Apr 8th 2005, 12:07 PMBobby BobInteresting Geometry Problem
Can anybody get this Geo Quiz,

Hint:

You need to add some lines. - Apr 8th 2005, 01:41 PMpaultwang
Is ABCD a square or just a parallelogram?

- Apr 8th 2005, 04:58 PMBobby BobSquare indeed
Sorry, Yes it is a square.

- Apr 8th 2005, 05:50 PMpaultwang
Here are all the relationships. Some are redundant.

F = J

G = N

M = K

S = P

R = Q

F + H + J = 180

G + M + S = 180

K + N + P = 180

Q + R + T = 180

H + K + M + T = 360

F + G = 90

J + N = 90

R + S = 90

P + Q = 90 - Apr 9th 2005, 08:47 AMBobby Bob
Cool but could you explain how you solved for angles M K and T.

You are not allowed to use Trig. sorry I didn't mention that earlier. - Apr 9th 2005, 09:02 AMpaultwang
When you draw that (green) line, with the properties of a square and an isosceles triangle, you created another isosceles triangle down there. The left triangle and the right triangle also become congruent. No trig is involved. This problem can be solved completely linearly.

- Apr 9th 2005, 10:56 AMBobby Bob
I still don't understand how you solved either angle M or angle T.

Once I understand your method I'll show you the way i did it.

Bob - Apr 9th 2005, 12:27 PMpaultwang
Honestly, I did not solve for any particular angles. I formed a 12-dimensional matrix with overdetermined equations, and performed gaussian elimination on it.

- Apr 10th 2005, 07:36 AMtheprofQuote:

Originally Posted by**Bobby Bob**

Proof.

If <ECD was not 60 then <BAE could not be 15.

http://theprof.altervista.org/75a.gif

PS

the other guy is wrong... :)

http://theprof.altervista.org/75b.gif - Apr 10th 2005, 05:24 PMBobby BobShow your work?
OK,

Paul and Prof,

Could you both post your work on how to solve this problem so that we can evaluate them both.

Bob - Apr 10th 2005, 08:48 PMpaultwang
Prof is right.

- Apr 11th 2005, 08:22 PMCoolerGeometric proof
These are the lines you need to add.

Sorry it is so messy.