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Areas of Parallelograms and Triangles
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16/07/2021 4:53 pm
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In Figure, AP || BQ || CR. Prove that ar(△AQC) = ar(△PBR).
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16/07/2021 4:54 pm
Given,
AP || BQ || CR
To Prove,
ar(AQC) = ar(PBR)
Proof:
ar(△AQB) = ar(△PBQ) — (i) (Since they are on the same base BQ and between the same parallels AP and BQ.)
ar(△BQC) = ar(△BQR) — (ii) (Since they are on the same base BQ and between the same parallels BQ and CR.)
Adding (i) and (ii),
ar(△AQB) + ar(△BQC) = ar(△PBQ) + ar(△BQR)
⇒ ar(△ AQC) = ar(△ PBR)