Simple geometry problem but only using geometry

[ovoleg]

THE PROBLEM

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!

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

 

[DaveC426913]

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?

 

[DaveC426913]

angle ABC = angle DCE

1] Your first line is false.

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

 

[ovoleg]

1] Your first line is false.

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

oh I am 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??

 

[rock.freak667]

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.

 

[tiny-tim]

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.

(oh … and use a protractor to draw the diagram, so that those angles look like 15º )

 

[Redbelly98]

Hello ovoleg,

Have you studied congruent triangles and theorems such as ASA, SSS, etc.?

 

[tiny-tim]

Bigger hint:

What is triangle

Spoiler

BFE

congruent to?