Question

Prove that the line segment joining the midpoints of the adjacent sides of quadrilateral form parallelogram.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

       Let ABCD be the quadrilateral and let P, Q, R, and S  be the midpoints of sides AB, BC, CD, and DA respectively.

           In ΔCDB, RQ || DB and RQ$=\frac{1}{2}$DB     (i)

              By midpoint theorem, then

                  In ΔADB, SP || DB and SP$=\frac{1}{2}$DB   (ii)

             By theorem (i) and (ii)

                          RQ||DB  and RQ=SP

         When a pair of opposite sides of PQRS are equal and parallel.

           Hence PQRS is a parallelogram.