Question

PQRS is a parallelogram. M and N are mid-points of PQ and QR. Diagonals PR and QS meet Prove that MONQ is a parallelogram.​

Answer 1

To prove MS II NQ

PROOF: In triangle PMS and triangle RNQ

angle MPS =angle NRQ ( opp. angle of IIgram)

PS = RQ ( opp. sides of IIgram)

PM =RN (given)

therefore , ∆PMS =∆RNQ ( by S.A.S)

MS = NQ ( by c.p.c.t.)

Now as PQ IIRS SO MQ II SN ( as MQ is a part of PQ and SN is of RS

NOW , as in quad. MQSN MQ II SN and MS = NQ

Therefore MQSN is a IIgram

therefore , MS II NQ

H. P.

Answer 2

To prove MS II NQ

PROOF: In triangle PMS and triangle RNQ

angle MPS =angle NRQ ( opp. angle of IIgram)

PS = RQ ( opp. sides of IIgram)

PM =RN (given)

therefore , ∆PMS =∆RNQ ( by S.A.S)

MS = NQ ( by c.p.c.t.)

Now as PQ IIRS SO MQ II SN ( as MQ is a part of PQ and SN is of RS

NOW , as in quad. MQSN MQ II SN and MS = NQ

Therefore MQSN is a IIgram

therefore , MS II NQ

H. P.