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 Jun, 2014, 01:23: PM

Expert Answer:

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  | 4th Jun, 2014, 03:23: PM