In the following figure, AP ⊥ BC, AD || BC, then Find A(∆ABC): A(∆BCD).
Given, AP ⊥ BC, and AD || BC. ΔABC and ΔBCD has the same base BC.
Areas of triangles with equal bases are proportional to their corresponding heights.
Since AP is the perpendicular distance between parallel lines AD and BC, the height of ΔABC and the height of ΔBCD are the same.
∴ `(A(ΔABC))/(A(ΔBCD)) = "AP"/"AP" = 1`
Hence A(ΔABC): A(ΔBCD) = 1: 1