# Math Help - A new Puzzle :)

1. ## A new Puzzle :)

Can anyone make 2 squares and 4 right-angled triangles using only 8 straight lines???

2. 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 . . .

3. 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...

4. 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.