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Q.

State whether the statement is true or false.
In a parallelogram ABCD, BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P, then ar (ΔBPC) = ar (ΔDPQ).


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a

True

b

False 

answer is A.

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Detailed Solution

Given that, in a parallelogram ABCD, BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P.
Given that,ABCD is a parallelogram and BC is produced to a point Q.
AD = CQ.
If AQ intersects DC at P, then ar (ΔBPC) = ar (ΔDPQ).
Question Image
Since ABCD is a parallelogram so, AB|| CD.
⇒AB||PC  
AD|| BC
⇒AD||CQ  
The triangles between the same parallel lines and on the common base, have equal areas. So,
ar(ΔAPC)=ar(ΔPBC)  .   [1]
We are given that AD = QC and AD ||QC. So,
ar(ΔDCQ)=ar(ΔACQ) On subtracting ar(ΔPCQ) from both sides, we get: ar(ΔDCQ)−ar(ΔPCQ)=ar(ΔACQ)−ar(ΔPCQ) ar(ΔDPQ)=ar(ΔAPC)                                           [2]  
From [1] and [2] we get area(ΔBPC) = area(ΔDPQ).
Hence, the given statement is true and the correct option is 1.
 
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