Simple geometry problem but only using geometry
THE PROBLEM
http://i295.photobucket.com/albums/m...athproblem.jpg given EAD = 15 degrees ADE = 15 degrees its a 10 by 10 square you can only use geometry to solve this problem, NO TRIGONOMETRY. Supposedly it can be done...I've been trying!! 3. The attempt at a solution angle ABC = angle DCE by symmetry angle EBC = angle ECB by symmetry angle ABC + angle EBC = angle DCE + angle ECB = 90 degrees angle AEB = 75 degrees = DEC angle AED = 150 degrees 
Re: Simple geometry problem but only using geometry
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2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical? 
Re: Simple geometry problem but only using geometry
Quote:
2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical? 
Re: Simple geometry problem but only using geometry
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Meant to say angle ABE! Can I try to approach this by assuming that BEC is not an equilateral triangle and try to prove it by contradiction?? 
Re: Simple geometry problem but only using geometry
angle AEB = Angle DEC 75 degrees
That is correct. But you are just given a square. and those angles of 15. Now if the base angles are both 15, what sort of triangle is that? When see what that is, you just need to remember the ways to show that triangles are congruent. 
make it symmetric …
Hi ovoleg!
Hint: scrub out lines BE and CE. Then make the diagram symmetric by drawing in the quadrilateral EFGH, where F G and H are defined in the same way as E. :smile: (oh … and use a protractor to draw the diagram, so that those angles look like 15º :frown:) 
Re: Simple geometry problem but only using geometry
Hello ovoleg,
Have you studied congruent triangles and theorems such as ASA, SSS, etc.? 
Bigger hint:
What is triangle
Spoiler
BFE

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