Question

Why are we constructing perpendicular bisectors to get the third vertex of the triangle?

Answer 1

The perpendicular bisectors are constructed, so as to get the required base angles. Suppose we want the base angles as 60^o 45^o. We initially construct arms at angles of 30^o and 22.5^o. So, now we construct the perpendicular bisectors to get the required base angles. This is based on the exterior angle property of a triangle, according to which the exterior angle of a triangle is equal to the sum of interior opposite angles.