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
 

Solution

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In POQ and ROSPOQ=ROS   [vertically opposite angle]OPQ=ORS    [alternate interior angle]POQROS   [By AA criterion]Hence, PORO=OQOS=PQRS      CPCT      ...(1)PORO=OQOSPORO+1=OQOS+1PO+RORO=OQ+OSOSPRRO=QSOSPRQS=ROOSPRQS=PQRS    [using 1]
  • 1
InPOQandROSPOQ=ROS[verticallyoppositeangle]OPQ=ORS[alternateinteriorangle]POQROS[ByAAcriterion]Hence,PORO=OQOS=PQRSCPCT...(1)PORO=OQOSPORO+1=OQOS+1PO+RORO=OQ+OSOSPRRO=QSOSPRQS=ROOSPRQS=PQRS[using1]
  • 1
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