Question

03. AP II BQ II CR. Prove that ar(AQC)=ar(PBR)​

Answer 1

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Two Triangles on the same base and between the same parallels are equal in area.

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Given,

AP || BQ || CR

To Prove,

ar(∆AQC) = ar(∆PBR)

Proof:

ar(△AQB) = ar(△PBQ) — (i)

(On the same base BQ and between the same parallels AP and BQ.)

also,

ar(△BQC) = ar(△BQR) — (ii)

 (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)

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