Question

using the postulate of drawing a circle, show that an equilateral triangle can be drawn with a given line segment as a side.

Answer 1

Draw a line segment, says PQ. Using Euclid’s postulate 3, draw a circle with center P and radius PQ.
Again, we draw another circle with center Q and radius QP.
The two circles meet at a point, says R.
Join P to R and Q to R. now, in  PQR, PQ = PR and PQ = QR.
So, by axiom 4, we get PQ = QR = PR.