Given three parallel lines, construct an equilateral triangle with a vertex on each line.
Hint? Something to try . . .
Prove your construction works for any three parallel lines. Is it a unique triangle?
Here is a presentation of three different constructions on one set of parallel lines. Are all three congruent equilateral triangles? Proof?
Given three parallel lines, construct an isosceles right triangle with one vertex on each of the three lines.