Question

prove that in any parallelogram, the point of the intersection of diogonals bysect each other​

Answer 1

Answer:

Let us consider a parallelogram ABCD such as diagonals AC and BD intersect at O

Also, in ||gm ABCD, AB = DC & AB || DC and AD = BC & AD || BC (known)

In triangles AOB and DOC

Angle BAO = Angle DCO (interior opposite angles)

AB = DC (Known)

Angle ABO = Angle CDO Interior opposite angles)

Hence, by ASA congruency, triangle AOB is congruent to triangle DOC

So, AO = CO and BO = DO

Thus the two diagonals bisect each other (Hence proved)