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Math Help - A new Puzzle :)

  1. #1
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    Question A new Puzzle :)

    Can anyone make 2 squares and 4 right-angled triangles using only 8 straight lines???
    Last edited by mr fantastic; October 11th 2009 at 06:32 PM. Reason: Removed link that promotes commercial website
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  2. #2
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    Hello, jeremyparker10!

    Can anyone make 2 squares and 4 right-angled triangles using only 8 straight lines?
    Spoiler:
    Code:
          * - - - * - - - *
          |     *   *     |
          |   *       *   |
          | *           * |
          *               *
          | *           * |
          |   *       *   |
          |     *   *     |
          * - - - * - - - *


    Spoiler:
    Code:
                      *
                    *   *
            * - - * - - - * - - *
            |   *           *   |
            | *               * |
            *                   *
          * |                   | *
        *   |                   |   *
      *     |                   |     *
        *   |                   |   *
          * |                   | *
            *                   *
            | *               * |
            |   *           *   |
            * - - * - - - * - - *
                    *   *
                      *

    Two squares and eight right triangles . . .
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  3. #3
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    Soroban, you can do much better:
    3 squares INSIDE a right triangle, with a total of 11 right triangles.
    The 3 squares are same size; large right triangle is isosceles.

    See next post...
    Last edited by Wilmer; October 13th 2009 at 06:38 AM. Reason: change 10 to 11 right triangles.
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  4. #4
    MHF Contributor
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    OK: 3 squares and 11 right triangles !

    Draw isosceles right triangle ABC: A(3,0), B(0,0), C(3,0). [3 lines]

    D and F on AB: D(0,1), F(0,2)
    H and J on BC: H(1,0), J(2,0)

    Draw FG and DE parallel to BC, G and E on AC. [2 lines]
    Draw HG and JE; will be parallel to AB. [2 lines]

    Let DE and GH intersect at K.
    So we have 3 1by1 squares: DBHK, KHJE and FDKG.

    Draw line FJ (will pass through K) [1 line]
    We now used up the 8 lines.

    You now have 11 right triangles:
    ABC, ADE, AFG, FBJ, FDK,FGK, GHC, GKE, KHJ, KEJ, EJC.

    --------------------------------------------------------------------------------------

    Better still: 5 squares and 12 right triangles.
    Easy:
    draw a square [4 lines]
    draw the diagonals [2 lines]
    draw the horizontal and vertical parallels [2 lines]

    That's it.
    4 squares inside larger square.
    4 right triangles created by the diagonals.
    8 right triangles created by the parallels.
    Last edited by mr fantastic; October 13th 2009 at 05:26 PM. Reason: Merged posts
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