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ABC and ABD are on the same base AB. If line segment CD is bisected by AB at O, show that ar (ABC) = ar(ABD)

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert

ABC and ABD are on same base AB

O is the mid point of CD (Given)

In ACD, AO is the median

ar (AOC) = ar (AOD) ...(I)

[Median divides a triangle into two triangles of equal area]

In BCD, BO is the median

ar (BOC) = ar (DOB) ...(II)

Adding I and II

ar(AOC) + ar(BOC) = ar(AOD) + ar (DOB) ...(III)

From III, ar (ABC) = ar(ABD)

Answered by Expert 4th June 2014, 3:23 PM
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