Question

In Fig. 15.82, ABC and ABD are two triangles on the base AB. If line segment CD is bisected by AB at O, Show that ar(Δ ABC) = ar(Δ ABD).

Answer 1

Given: ABC and ABD are two triangles on the base AB and the line segment CD is bisected by AB at O.  

 

To show:

ar (ABC) = ar (ABD).

 

Proof:

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

OC= OD

In ∆ACD, we have OC = OD

So, AO is the median of ∆ACD

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

 ∴ ar(∆AOC) = ar(∆AOD) ……….. (i)

 

Similarly,In ΔBCD,

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

∴ ar(∆BOC) = ar(∆BOD) ……….. (ii)

 

On Adding eq (i) and (ii) we get,

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

ar(∆ABC) = ar(∆ABD)

HOPE THIS ANSWER WILL HELP YOU…..

 

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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)+ar(BOD)

⇒ ar(ABC) = ar(ABD)

Hence showed.