# A new Puzzle :)

• Oct 11th 2009, 03:06 PM
jeremyparker10
A new Puzzle :)
Can anyone make 2 squares and 4 right-angled triangles using only 8 straight lines???
• Oct 12th 2009, 05:38 PM
Soroban
Hello, jeremyparker10!

Quote:

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 . . .
• Oct 12th 2009, 11:00 PM
Wilmer
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...
• Oct 13th 2009, 07:37 AM
Wilmer
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.

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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.