PQRS is a trapezium such that PQ||SR. The ratio PR:QS is always equal to 1) PQ:SR 2) PO-OR:QO-OS 3) PO+OR:QO-OS 4) PO^2:OQ^2 Share with your friends Share 3 Gajendra answered this Solution 23 View Full Answer Vansh Narula answered this In △POQ and △ROS∠POQ=∠ROS [vertically opposite angle]∠OPQ=∠ORS [alternate interior angle]∴△POQ≅△ROS [By AA criterion]Hence, PORO=OQOS=PQRS CPCT ...(1)⇒PORO=OQOS⇒PORO+1=OQOS+1⇒PO+RORO=OQ+OSOS⇒PRRO=QSOS⇒PRQS=ROOS⇒PRQS=PQRS [using 1] 2 Vansh Narula answered this In△POQand△ROS∠POQ=∠ROS[verticallyoppositeangle]∠OPQ=∠ORS[alternateinteriorangle]∴△POQ≅△ROS[ByAAcriterion]Hence,PORO=OQOS=PQRSCPCT...(1)⇒PORO=OQOS⇒PORO+1=OQOS+1⇒PO+RORO=OQ+OSOS⇒PRRO=QSOS⇒PRQS=ROOS⇒PRQS=PQRS[using1] 2
