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

Question

Philoid · Accepted Answer

Since ΔABQ and ΔPBQ lie on the same base BQ and are between the same parallels AP and BQ

Area (ΔABQ) = Area (ΔPBQ) (i)

Again, ΔBCQ and ΔBRQ lie on the same base BQ and are between the same parallels BQ and CR

Area (ΔBCQ) = Area (ΔBRQ) (ii)

On adding equations (i) and (ii), we obtain

Area (ΔABQ) + Area (ΔBCQ) = Area (ΔPBQ) + Area (ΔBRQ)

Area (ΔAQC) = Area (ΔPBR)