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If D is the mid-point of the hypotenuse ...

`If` D is the mid-point of the hypotenuse `A C` of a right triangle `A B C` , prove that `B D=1/2A C` . GIVEN : A `A B C` in which `/_B=90^0` and `D` is the mid-point of `A Cdot` TO PROVE : `B D=1/2A C` CONSTRUCTION Produce `B D` to `E` so that `B D=D Edot` Join `E Cdot`

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`In /_ADB and /_CDE`
`AD=CD`(O is midpoint of AC)
`BD=DE`(given)
`/_ADB=/_CDE`(UDA)
`/_ADB cong /_CDE(SAS)`
`EC=AB and /_CED=/_ABP`
`In /_ABC and /_ECB`
`AB=EC`(proved above)
...
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