Question

ABC and DBC are two Triangles on same base BC If a line segment bisected AB at O show ar.ABC=ar.ABD​

Answer 1

Answer:

ΔABC and ΔABD are two triangles on the same base AB.

To show :

ar(ABC)=ar(ABD)

Proof :

Since the line segment CD is bisected by AB at O. OC=OD.

In ΔACD, We have OC=OD.

So, AO is the median of ΔACD

Also we know that median divides a triangle into two triangles of equal areas.

∴ar(ΔAOC)=ar(ΔAOD) _______ (1)

Similarly , In ΔBCD,

BO is the median. (CD bisected by AB at O)

∴ar(ΔBOC)=ar(ΔBOD) _______ (2)

On adding equation (1) and (2) we get,

ar(ΔAOC)+ar(ΔBOC)=ar(ΔAOD)+ar(ΔBOD)

∴ar(ΔABC)=ar(ΔABD)