Question

29. In the given figure, AP || BQ || CR.prove that
area (∆AQC) = area (∆PBR).​

Answer 1

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Answer 2

Answer:

ar(AQC) = ar(PBR)

Hence Proved

Step-by-step explanation:

Given: AP II BQ II CR

To prove: ar(AQC) = ar(PBR)

Proof:   In the given Figure,

         

          ar(ABQ) = ar(PBQ)                        - ( eq 1)

Since, these triangles are on the same base BQ and between the same parallels BQ and AP.

Similarly,

        ar(CBQ) = ar(RBQ)                         - (eq  2)

Since, these triangles are on the same base BQ and between the same parallels BQ and CR.

Now,

Adding (eq 1) and (eq 2) we get,

=> ar(AQB) + ar(BQC) = ar(PBQ) + ar(QBR)

=> ar(AQC) = ar(PBR)

   Hence proved.