# Interesting Geometry Problem

• Apr 8th 2005, 12:07 PM
Bobby Bob
Interesting Geometry Problem
Can anybody get this Geo Quiz,

Hint:

You need to add some lines.
• Apr 8th 2005, 01:41 PM
paultwang
Is ABCD a square or just a parallelogram?
• Apr 8th 2005, 04:58 PM
Bobby Bob
Square indeed
Sorry, Yes it is a square.
• Apr 8th 2005, 05:50 PM
paultwang
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 AM
Bobby 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 AM
paultwang
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 AM
Bobby 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 PM
paultwang
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 AM
theprof
Quote:

Originally Posted by Bobby Bob
Can anybody get this Geo Quiz,

Hint:

You need to add some lines.

The answer is 60.
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 PM
Bobby Bob
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 PM
paultwang
Prof is right.
• Apr 11th 2005, 08:22 PM
Cooler
Geometric proof
These are the lines you need to add.

Sorry it is so messy.