Prove that the diagonals of a rhombus are perpendicular bisectors of each other.

Explanation

Let `ABCD` is a rhombus.

`=>AB=BC=CD=DA "[ Adjacent sides are eqaul in rhombus ]"`

In `triangle AOD \ and \ triangle COD`
`=>OA=OC " [ Diagonals of rhombus bisect each other ]"`

`=> OD=OD " [ Common side ]"`

`=> AD=CD `
so, `triangle AOD ~= triangle COD`
`=> angle AOD= angle COD`
`=> angle AOD+ angle COD=180^o`
`=>2 angle AOD= 180^o`
`=>angle AOD =90^o`
Hence the diagonals of a rhombus bisect each other at right angles.