# How to make 4 triangles out of 4 lines

Use any drawing software like Paint or the like to draw 4 triangles using only 4 straight lines! Also, the borders of your drawing don't count ;)

I think you can draw

any four straight lines.

(As long as no two of them are parallel with each other, and all the six crossing points are distinct from each other.)

This works, because

any three straight lines will always form a triangle, unless either
* some two of the lines don't ever cross (because they are parallel), or
* all three lines cross at the same point.

Since you have 4 lines, you can

choose three of them in 4 separate ways,

so you are guaranteed to always get exactly 4 triangles.

• Nitpick: this seems to assume an infinite space, which Paint is not.
– Mark
Commented Jan 17, 2020 at 13:07
• @Mark to escape the nitpick on a technicality: the puzzle explicitly says that the borders don't count :-)
– Bass
Commented Jan 17, 2020 at 13:44
• I think that means they don't count as edges of the triangle (somehow I can't tag you sorry)
– Mark
Commented Jan 17, 2020 at 13:46
• @Mark I agree 100%, but I'm going to plead the letter of the law :-) (The poster will automatically get a notification of any comment added to their post, so tagging me here isn't necessary, which is also why it doesn't work.)
– Bass
Commented Jan 17, 2020 at 13:53
• @mark you don't need an infinite space (it is never even mentioned in the answer). Commented Jan 17, 2020 at 14:30

Here's a solution for 4 triangles with 4 straight lines:

Here are the first two triangles:

Here's the third triangle:

Here's the fourth triangle:

In fact,

I suspect that this will work for any triangle formed of three lines with an additional line, so long as the additional line is not parallel to any of the three other lines nor incident to the vertices of the triangle.

• Regarding the final spoiler block: I don't think it's necessary for the fourth line to cross the triangle. Using your diagram as an example: if you draw the lines forming the smallest triangle first, the fourth line doesn't cross it, but everything still works. (I may have also posted an answer to this effect before reading yours all the way to the end.)
– Bass
Commented Jan 16, 2020 at 21:45
• @Bass Good point, I'll revise my answer to include that point.
– Avi
Commented Jan 16, 2020 at 21:47

My solution to this is as follows:
- ABE
- DBF
- CEF

• I like this answer best, simple and effective. Live long, and prosper. Commented Jan 17, 2020 at 21:19

The four triangles are:
- ABC