Simple geometry problem but only using geometry

  1. THE PROBLEM
    [​IMG]
    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
     
  2. jcsd
  3. DaveC426913

    DaveC426913 16,128
    Gold Member

    1] Your first line is false.

    2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical?
     
  4. DaveC426913

    DaveC426913 16,128
    Gold Member

    1] Your first line is false.

    2] Can you elaborate on this 'symmetry' for me? Show why they're symmetrical?
     
  5. 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??
     
  6. rock.freak667

    rock.freak667 6,228
    Homework Helper

    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.
     
  7. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    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:)
     
  8. Redbelly98

    Redbelly98 12,034
    Staff Emeritus
    Science Advisor
    Homework Helper

    Hello ovoleg,

    Have you studied congruent triangles and theorems such as ASA, SSS, etc.?
     
  9. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    Bigger hint:

    What is triangle
    BFE
    congruent to? :smile:
     
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