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anonymous

  • 4 years ago

Please help.I am confused! Inside a square ABCD construct the equilateral triangles ABK,CDM,and DAN.Prove that the midpoints of the segments KL,LM,MN,NK and those of AN,AK,BK,BL,CL,CM,DM, and DN are the vertices of a regular dodecagon.

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  1. anonymous
    • 4 years ago
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    u have a picture?

  2. Directrix
    • 4 years ago
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    Wondering where the points K, M, and N are located?

  3. jhonyy9
    • 4 years ago
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    yes one picture may be importantly --- i think

  4. Directrix
    • 4 years ago
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    Click on "Draw" and sketch it , please.

  5. anonymous
    • 4 years ago
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    L is an arbitrary point?

  6. anonymous
    • 4 years ago
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    I think you forgot a triangle BCL

  7. jhonyy9
    • 4 years ago
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    |dw:1328433505949:dw|

  8. jhonyy9
    • 4 years ago
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    so this is like there this ?

  9. anonymous
    • 4 years ago
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    I think it's something like this.

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  10. anonymous
    • 4 years ago
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    I'll try to solve this.

  11. jhonyy9
    • 4 years ago
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    SqueeSpleen --- ATTENTION --- this exersice begin with the word ,,inside a square ..." - so i think that in this way your picture not can being right,correct how do you think ?

  12. anonymous
    • 4 years ago
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    Inside... :( I'm horrible with English. I'll make a new draw.

  13. anonymous
    • 4 years ago
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    Now it's correct?

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  14. anonymous
    • 4 years ago
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    yes

  15. anonymous
    • 4 years ago
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    We can Prove Angles are equal all of them it is very easy onlt the figure is complicated

  16. anonymous
    • 4 years ago
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    Distances neednot be found

  17. anonymous
    • 4 years ago
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    I have a proof using complex numbers but I want a purely geometric proof.

  18. anonymous
    • 4 years ago
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    I'm wanting to use trigonometry :p, that's why I'm using distances to figure out the angles.

  19. anonymous
    • 4 years ago
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    KM=(1-2(1-cos(30)))CB distance between mid point kn and midpoint nm=KM/2 I forget the parenthesis. the first time.

  20. anonymous
    • 4 years ago
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    Take only two adjacent angle and try to proof them equal I have done it Then you can use symetry argument to extend it to all adjacent pairs

  21. anonymous
    • 4 years ago
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    Label all points and I shall show you

  22. anonymous
    • 4 years ago
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    I'm horrible with geometry but I'll label all points and left it to you. Geometry problems were the problems who gave me the worst times when I was in my countrys maths olympiads :( I named the mid points of the segments after their extrems.

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