Question

plz solve this question ​

Answer 1

     

Consider ΔACD.

DS : SA = DR : RC = 2 : 1

We know that if a line cuts two sides of a triangle in the same ratio, then it will be parallel to the third side.

∴ RS ║ AC   →   (1)

Consider ΔABC.

AP : PB = CQ : QB = 1 : 2

PQ ║ AC   →   (2)

From (1) and (2),

PQ ║ RS

Draw diagonal BD.

Consider ΔBCD.

CQ : QB = CR : RD = 1 : 2

∴ QR ║ BD   →   (3)

Consider ΔABD.

AS : SD = AP : PB = 1 : 2

∴ PS ║ BD   →   (4)

From (3) and (4),

PS ║ QR

Consider quadrilateral PQRS.

We got that  PQ ║ RS  and  PS ║ QR.

∴ PQRS is a parallelogram.

Hence proved.

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Answer 2

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... Please try to understand (^^)