Question

using vectors prove that the diagonals of a parallelogram bisect each other​

Answer 1

Answer:

Take a parallelogram as ABCD with centre point as O

Step-by-step explanation:

We have to prove diagonals of parallelogram ABCD bisects each other.

i.e, OA=OC & OB=OD

Now In ΔAOD and ΔBOC

AD=BC [opposite sides are equal]

∠ADO=∠CBO [alternate interior angle]

Similarly ∠DAO=∠BCO

∴ΔAOD≅ΔBOC by (ASA rule)

So, OA=OC & OB=OB [ By CPCT]

Answer 2

Answer:

so I tried solving this problem and ended up with the solution as:showed this by showing that two diagonals intersect at midpoints.

Step-by-step explanation:

let A,B,C,D, be the four sides ;then if the vectors are oriented as shown in the figure below we have A+B=C+D thus two opposite side are equal and parallel , which shows the figure is a parallelogram.