Triangles??

Question

How do you make the most triangles you can with only 6 or 8 straight line for the whole group of triangles??

Answer 1

A little difficult to interpret this question, but if you mean how can I draw six straight lines and form the maximum number of triangles, I would assume you'd draw a triangle with three of your lines, then draw a line from each corner to the middle of the opposite side. You end up with 16 triangles of various sizes.

If on the other hand the lines can't cross but are three-dimensional (eg you're building it out of matchsticks) then make a tetrahedron and you get 4 triangles.

8 lines is a completely different question.

Answer 2

4

Answer 3

If you don't count mirror image triangles separately then it's just a matter of counting the combinations of 3 in 6, then 3 in 8. And there are no 2 lines of the same length.
6x5x4/(3x2x1)=20 and 8x7x6/(3x2x1)=56.
20 different triangles with 6 unique lines and
56 different triangles with 8 unique lines.

Answer 4

Are the lines as long as you want? You can try reasoning like this: starting with three, where can you add the fourth to make the most? Starting with the most for four, where can you add the fifth to make the most? Don't forget to extend the lines (if they can be as long as you want) to get "outside" triangles.

Answer 5

It is a question of permutation and combination and especially combination.

Look to make a triangle you need 3 straight lines.

6C3,

8C3

Answer 6

A square with an asterisk in it.