By using the concept of slope, prove that the diagonals of a rhombus are at right angles.

Explanation

Let `A B C D` is a rhombus.

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

In `triangle AOD` and `triangle COD`

`Rightarrow OA=OC `[Diagonals of rhombus bisect each other]

`Rightarrow OD=OD ` [Common side]

`Rightarrow AD=CD`

`triangle AOD cong triangle COD ` [ By SSS congruence rule]

`Rightarrow angle AOD=angle COD [CPCT]`

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