Hello, jeremyparker10!
Can anyone make 2 squares and 4 right-angled triangles using only 8 straight lines?Spoiler:
Spoiler:
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...
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.