ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O,
show that area(△ABC) = area(△ABD). [2 MARKS]
Concept : 1 Mark
Application : 1 Mark
Consider △ACD.
Line-segment CD is bisected by AB at O. Therefore, AO is the median of △ACD.
So, Area (△ACO) = Area (△ADO) ... (1)
Considering △BCD, BO is the median.
So, Area (△BCO) = Area (△BDO) ... (2)
Adding equations (1) and (2), we obtain
Area (△ACO) + Area (△BCO) = Area (△ADO) + Area (△BDO)
Area (△ABC) = Area (△ABD)