Question

prove that an equilateral triangle can be drawn from a given line segment

Answer 1

cut the line in 3 equal part and form a triangle it will bw equilateral

Answer 2

let given line is AB
Place the tip of the compass on point A, and open it up so that you can draw an arc across point B.

Your compass radius is now set to the length AB.

Keeping the radius the same, place the tip of the compass on point A again, and draw an arc on the paper above your segment.

Place the tip of the compass on point B now, again using the same radius, an draw another arc that intersects the first arc. The point of intersection is point C.

Now use your straightedge to draw line segments AC and AB.