In the given figure,PQRS is a parallelogram. The bisector of angle PQR and angle QPS meet PS produced and QR produced at X,Y respectively show that PQ = XY. Share with your friends Share 21 Brijendra Pal answered this Hi, In the triangle XPQPY and QX are bisector of angle QPS and PQR, soangle XPY = angle QPY....1 also PX∥QYso angle QYP = angle YPX Alternate interior angle using equation 1, angle QPY= angle QYP so in triangle QPY PQ = QY....2similalrly, in triangle QPY PX∥QYso angle PXQ = angle YQX Alternate interior angle ....3also QX is bisector of angle PQY so angle XQY = angle PQX combining this with equation 3angle PXQ = angle PQX so PQ = PX .....4from equation 2 and 4 PX = QYnow since PX∥QY and PX = QY so PQXY is a parallelogram so PQ = XY 3 View Full Answer
