## Simple geometry problem but only using geometry

THE PROBLEM

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

 Quote by ovoleg angle ABC = angle DCE by symmetry
1] Your first line is false.

2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical?

 Quote by ovoleg angle ABC = angle DCE
1] Your first line is false.

2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical?

## Simple geometry problem but only using geometry

 Quote by DaveC426913 1] Your first line is false. 2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical?
oh im sorry typo!!

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??
 Recognitions: Homework Help 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.
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor 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. (oh … and use a protractor to draw the diagram, so that those angles look like 15º )
 Mentor Blog Entries: 10 Hello ovoleg, Have you studied congruent triangles and theorems such as ASA, SSS, etc.?
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor Bigger hint: What is triangle Spoiler BFE congruent to?