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A D and B C are equal perpendiculars to ...

`A D` and `B C` are equal perpendiculars to a line segment `A B` . Show that `C D` bisects `A Bdot`

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Given that
AD and BC are equal perpendiculars to a line segment AB
To prove `C D` bisects `AB`
proof
Two triangles `triangleAOD` and `triangle BOC`
`angle AOD = abgle BOC` {Vertically opposite angles}………………. (i)
`angle OAD = angle OBC` {Given that they are perpendiculars}…. (ii)
`AD = BC` {As given}………… (iii)
From above three equation both the triangle satisfies “AAS” congruency criterion
So,` triangleAOD cong triangle BOC`
`AO` and` BO `will be equal as they are corresponding parts of congruent triangles(CPCT).
So, `AO = BO`
Hence, `CD `bisects `AB` at `O`.
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