In Fig., AP || BQ || CR. Prove that ar.(AQC) = ar.(PBR).

1.	In Fig., AP \|\| BQ \|\| CR. Prove that ar.(AQC) = ar.(PBR).
Answer» Data: AP \|\| BQ \|\| CR. To Prove: ar.(∆AQC) = ar.(∆PBR) Proof: AP \|\| BQ. CR is a line segment. ∆ABQ and ∆PBQ are on base BQ and in between AP \|\| BQ ar.(∆ABQ) = ar.(∆PBQ) ………….. (i) ∆BQC and ∆BQR are on base BQ and in between BQ \|\| CR. ∴ ar.(∆BQC) = ar.(∆BQR) ………….. (ii) Adding (i) and (ii), ar.(∆ABQ) + ar.(∆BQC) = ar.(∆PBQ) + ar.(∆BQR) ∴ ar.(∆AQC) = ar.(∆PBR).

Answer»

Data: AP || BQ || CR.

To Prove: ar.(∆AQC) = ar.(∆PBR)

Proof: AP || BQ. CR is a line segment.

∆ABQ and ∆PBQ are on base BQ and in between

AP || BQ ar.(∆ABQ) = ar.(∆PBQ) ………….. (i)

∆BQC and ∆BQR are on base BQ and in between BQ || CR.

∴ ar.(∆BQC) = ar.(∆BQR) ………….. (ii)

Adding (i) and (ii),

ar.(∆ABQ) + ar.(∆BQC) = ar.(∆PBQ) + ar.(∆BQR)

∴ ar.(∆AQC) = ar.(∆PBR).

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