Given:    is an isosceles triangle.

                P,Q and R are the midpoints of the segments  respectively.

Prove:    Midpoints P,Q and R forms an isosceles triangle.

Proof:   Use midpoint formula to find the coordinates of midpoints of P, Q and R.

              Coordinates of P

              Coordinates of Q

             Coordinates of R

             The coordinates of P, Q and R are , and respectively.

             If the measures of two sides of a triangle are same then the triangle is isosceles.

             Now find the distance of  using distance formula.

Since , the triangle PQR is an isosceles triangle.

Triangle PQR is isosceles triangle.