Question

Prove that an equilateral triangle can be constructed on any given line segment.
prove with a rough figure

Answer 1

Solution : In the statement above, a line segment of any length is given, say AB
Here, you need to do some construction. Using Euclid’s Postulate 3, you can draw a
circle with point A as the centre and AB as the radius.Similarly, draw
another circle with point B as the centre and BA as the radius. The two circles meet at
a point, say C. Now, draw the line segments AC and BC to form Δ ABC.
So, you have to prove that this triangle is equilateral, i.e., AB = AC = BC.
Now, AB = AC, since they are the radii of the same circle (1)
Similarly, AB = BC (Radii of the same circle) (2)
From these two facts, and Euclid’s axiom that things which are equal to the same thing
are equal to one another, you can conclude that AB = BC = AC.
So, Δ ABC is an equilateral triangle.

Answer 2

I think it will help you