Question

if O is a point in the interior of parallelogram ABCD, then show that area of triangle OAB + area of triangle OCD =area of triangle OAD+ area of triangle OBC

Answer 1

Here is your Proof.
I solved this question last year in my classroom and as well as in my coaching centre.

I requires some construction.

Happy to help you. ✌

Answer 2

Answer:

Step-by-step explanation

given,

abcd is parallelogram

to show,

area of triangleoab+ ar of triangle ocd = area of triangle oad + area of triangle obc.

proof,

in ttriangle oab and ocd,

ab=cd                     (side of parallelogram)

o=o                          (common)

angle a= angle d       opposite angles are equal

tri oab = ocd              {asa}

similarly,

tri oad = tri obd         {by cpct}

tri aob + ocd = tri oad + obc                [proved above}