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Show that the diagonals of a rhombus bis...

Show that the diagonals of a rhombus bisect each other at right angles.

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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.
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  • The diagonals of a rhombus bisect each other at _____ angles.

    A
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    B
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    C
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    D
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