In Fig.9.28, AP || BQ || CR. Prove that ar(△AQC) = ar(△PBR).

Solution:

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.)

also,

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)