Question

the triangles abc and abd are on the same base ab . if cd intersects ab at o .prove yhat area of triangle abc to that of abd is equal to oc:do.​

Answer 1

Ex 9.3, 4 In figure, ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD). ... same base AB & AB bisects CD, i.e. , OC = OD To prove: ar (ABC) = ar (ABD) Proof : In Δ ACD, Since OC ... Ex 9.3, 4 - Chapter 9 Class 9 Areas of Parallelograms and Triangles.

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.