the figure a, b ,c and d are points on the sides of a quadrilateral pqrs such that this point divides p q, r q, r s and p s in the ratio 2 : 1 prove that ABCD is a parallelogram Plzz answers fast
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In ∆PSR and ∆DSZ DS/PS =SC/SR=1/3
< S is Common
∆PSR~∆DSZ
<SDZ =<SPR
DC || PR.................(1)
Similarly. we can say that
∆AQB~∆PQR
Thus AB||PR.................(2)
Also we can say that
∆CRB~∆SRQ
BC || QS..............(3)
∆PDA ~∆PSQ
AD || QS..........(4)
Now in quad ABCD
AB||CD [ Combining (1) & (2)]
BC || AD [ Combining (3) &(4) ]
since the opposite side s are ||
quad ABCD Is a || gm
< S is Common
∆PSR~∆DSZ
<SDZ =<SPR
DC || PR.................(1)
Similarly. we can say that
∆AQB~∆PQR
Thus AB||PR.................(2)
Also we can say that
∆CRB~∆SRQ
BC || QS..............(3)
∆PDA ~∆PSQ
AD || QS..........(4)
Now in quad ABCD
AB||CD [ Combining (1) & (2)]
BC || AD [ Combining (3) &(4) ]
since the opposite side s are ||
quad ABCD Is a || gm
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