Question

In figure ABC and ADC are two triangles on the same base ab if line segment CD is bisected by ab at a show that area ABC is equal to area in ABD.
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Answer 1

Step-by-step explanation:

Given

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)

I hope that's helpfull so mark me brainlist.

Answer 2

In triangle ABC, AO is the median (CD is bisected by AB at O)

So, ar(AOC)=ar(AOD)..........(i)

Also,

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

So, ar(BOC) = ar(BOD)..........(ii)

Adding (i) and (ii),

We get,

ar(AOC)+ar(BOC)=ar(AOD)+(BOD)

⇒ ar(ABC) = ar(ABD)

Hence showed.