Question

Prove that an equilateral triangle can be constructed on any given line through two points.

Answer 1

Equilateral triangle is a angel with all sides are equal

1. Draw a line segment AB of the any length.

2. Take compass put the pointy end at point A & pencile at point B.

3.Draw an arc.

Here we draw an arc of radii AB

4. Now put the pointy end at B and pencil at A.

5. Draw another arc.

Here we draw an arc of radii BA .

6. Mark the intersecting point as C.

7. Join point A to point C by a straight line .

8. Join point B to point C by a straight line

$ABC$ is the triangle.