Question

In the given figure, AP $\parallel$ BQ $\parallel$ CR. Prove that ar ($△$AQC) = ar ($△$PBR).
[2 MARKS]

Answer 1

Concept : 0.5 Mark
Application : 0.5 Mark
Calculation : 1 Mark

Since $△$ABQ and $△$PBQ lie on the same base BQ and are between the same parallels AP and BQ,

$\therefore$ Area ($△$ABQ) = Area ($△$PBQ) ... (1)

Again, $△$BCQ and $△$BRQ lie on the same base BQ and are between the same parallels BQ and CR.

$\therefore$ Area ($△$BCQ) = Area ($△$BRQ) ... (2)

On adding equations (1) and (2), we obtain

Area ($△$ABQ) + Area ($△$BCQ) = Area ($△$PBQ) + Area ($△$BRQ)

$\Rightarrow$ Area ($△$AQC) = Area ($△$PBR)