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A triangle A B C is an isosceles tria...

A triangle `A B C` is an isosceles triangle if any one of the following conditions hold: Bisector of `/_B A C` is perpendicular to the base `B C`

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In `/_\ ADB and ADC`
`/_BAD=/_CAD`
AD is bisector of `/_B A C`
AD=AD
`/_\ ADB=/_\ ADC` (Each equal to 90^0)
`/_\ ADB~=`/_\ ADC (By ASA congruence Criterion
`AB=AC`(CPCT)
Hence, triangle ABC is isosceles.
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