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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. |
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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` |
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