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Question

ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, area of ABC equals to area of_______.

A
ADB
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B
AOD
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C
BOD
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D
AOC
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Solution

The correct option is A ADB

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)


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