Question

prove that the digonals of a parallelogram bisect each other
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Answer 1

I think the answer helps you

Answer 2

Answer:

to prove this you will have to take help of congruency of triangles

please make a diagram to understand it in a better way.

let ABCD be a parallelogram (ABCD in cyclic order)

let diagonals AC and BD intersect at O.

to prove

1. OA = OC

2. OB = OD

In ∆ AOB and ∆ COD

AB = CD ( opposite sides of a parallelogram)

angle OAB = angle OCD (alternate interior angle)

angle OBA = angle ODC ( as above)

hence ∆ AOB is congruent to ∆ COD by ASA

hence, other corresponding parts of the two triangles will be equal

so OA = OC

and OB = OD

i.e. O is the mid point of both AC and BD

thus diagonals of a parallelogram bisect each other