Question

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]

Answer 1

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)