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Question

# In the given figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).

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Solution

## Consider ΔACD. Line-segment CD is bisected by AB at O. Therefore, AO is the median of ΔACD. ∴ Area (ΔACO) = Area (ΔADO) ... (1) Considering ΔBCD, BO is the median. ∴ Area (ΔBCO) = Area (ΔBDO) ... (2) Adding equations (1) and (2), we obtain Area (ΔACO) + Area (ΔBCO) = Area (ΔADO) + Area (ΔBDO) ⇒ Area (ΔABC) = Area (ΔABD)

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