how do you make 6 congruent lines to make 4 equilateral triangles?

Answer 1

Sure, it's a solid, 4-sided pyramid where each side is an equilateral triangle (tetrahedron - see link pic).

I believe there's a planar answer too which you can draw with two triangles, one upside down and slightly offset - which also looks like two bowties on top of each other.

Answer 2

Here's one way:

Draw a big equilateral triangle. Label the midpoints of each side "A", "B" and "C". Now draw a line from B to C and extend it until it's the same length as one of the triangle sides. Do the same with a line from B to A. Now connect the two end points of this "V" shape you just drew. You'll have two overlapping equilateral triangles. This is also 6 congruent lines that make 4 smaller equilateral triangles (plus a parallelogram in the middle).

Answer 3

Make one triangle ABC out of 3 lines (of equal length). and another DEF. Put point F on the midpoint of line AB and C on the midpoint of DE so that the two triangles are superimposed on each other - the two bases are parallel to each other. The corners will give you four equilateral triangles with a diamond shape in the middle.

Answer 4

Try a 3 sided pyramid

Answer 5

Make them into a tetrahedron.