Question

Solve these question....

Answer 1

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Answer 2

Given: Ar(DRC)=Ar(DPC) Ar(BDP)=Ar(ARC)
To prove: ABCD & DCPR are trapeziums..
Proof: Triangle DPC and DRC lie on the same base DC and are equal in area and they lie in between DC&PR....hence DC||PR..
In DCPR one pair of opposite sides of quadrilateral are parallel..
Hence, DCPR is a trapezium..

Ar(BDP)=Ar(ARC).......(1)
Ar(DPC)=Ar(DRC).......(2) (as per the proof above)
Now, subtracting (2) from (1) we get..
Area BDC = Area ADC..
Now..Triangle BDC and ADC area equal in area hence..so AB||CD...in ABCD one pair of opposite sides of quadrilateral are parallel..
Hence, ABCD is a trapezium..


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