Question

PQRS is a trapezium in which PQ || SR and PS = QR. It A,B,C,D be respectively the midpoints of QP, QS,RS and RP , then show that ABCD is a rhombus​

Answer 1

Answer:

Step-by-step explanation:

IN PQRS,QandRarethemidpointsofBDandCDrespectively.QR∥BCandQR=21​BC[AccordingtoMidpointTheorm]In△ABC,PandSaremidpointsofBAandACrespectively.Similarly,PS∥BCandPS=21​BC(AccordingtoMidpointTheorm)∴PS∥QRandPS=QR[Eachequalto21​BC]∴PQRSisaparallelogram.In△ACD,SandRarethemidpointsofACandCDrespectively.SR∥ADandSR=21​AD=21​BC[∵AD=BC(Given)]∴PS=QR=SR=PQ.Hence,ABCDisarhombus