1.

PQRS is a parallelogram. PS is produced to M, so that SM = SR and MR produced meets PQ produced at N. Prove that QN = QR.

Answer» With the given details, we can create a diagram. Please refer to video for the diagram.
From the figure,`SM||QR||PS`
`:. /_QRN =/_SMR`
Also, `PQ||SR||QN`
`:./_RSM = /_RQN`
In `Delta RSM and Delta NQR`,
`/_QRN =/_SMR`
`/_RSM = /_RQN`
As two of their angles are equal, third angle will also be equal. So, `Delta RSM ~=Delta NQR`
`:. (SM)/(QR) = (SR)/(QN)=> (SM)/(SR)= (QR)/(QN)`
As, `SM =SR` , it means ,`QR = QN`


Discussion

No Comment Found