Question

prove that a quadiletral formed by joining the midpoints of a quadleteral is a parellogram.​

Answer 1

Answer:

(i) In ΔDAC,

R is the mid point of DC and S is the mid point of DA.

Thus by mid point theorem, SR || AC and SR = 1/2 AC

(ii) In ΔBAC,

P is the mid point of AB and Q is the mid point of BC.

Thus by mid point theorem, PQ || AC and PQ = 1/2 AC

also, SR = 1/2 AC

Thus, PQ = SR

(iii) SR || AC - from (i)

and, PQ || AC - from (ii)

⇒ SR || PQ - from (i) and (ii)

also, PQ = SR

Thus, PQRS is a parallelogram