Question

prove that diagonals of parlellogram divides parallelogram into two equal parts

Answer 1

ABCD is a parallelogram and BD is one of its diagonals.

As we know the opposite side of parallelograms are equal,

∴AB = CD and AD= BC

In ΔABD and ΔCDB,

AB= CD( given)

AD= BC (given)

BD= BD (common side)

∴ ΔABD  ΔCDB ( By SSS congruencyrule)

Similarly, we can prove ΔABC  ΔCDA.

We know that congruent triangles have equal areas.

 ar(ΔABD) = ar(ΔCBD)and ar(ABC) = ar(ΔCDA)ar∆ABD = ar∆CBDand arABC = ar∆CDA

Hence, the diagonal of a parallelogram divides it into 2 congruent triangles of equal areas.