Question

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).​

Answer 1

Answer:

The Perpendicular bisector theorem states that the when a line is bisected by an another line the Opposite angles formed by the intersection will be equal

So that means angle aoc and angle aob will be equal. So the angle adjactent to them will be as follows

Let angle aoc be x so aob will also be beacuse of the  perpendicular bisector theorem now the adjacent angles.. The adjacent angles will be 180 - x

.since the angles are equal the triangles will be of same proportions and are having similar sides, their areas are equal.

Step-by-step explanation:

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.