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

A triangle `A B C` is an isosceles triangle if any one of the following conditions hold: Altitude `A D` bisects `/_B A C` Bisector of `/_B A C` is perpendicular to the base `B C`
In triangle,`A B C`
let the altitude AD bisects `/_BAC`
Then we have to prove that the triangle ABC, is isosceles.
In `/_\`s ADB and ADC`,
`/_BAD=/_CAD`
(AD is bisector of`/_BAC)`
`AD=AD`(common)
`/_ADB=/_ADC` (Each equal to 90)
`=>/_\ADB~=/_\ADC` (by ASA congruence criterion)
`AB=AC`(cpct)
Hence, A triangle `A B C` is an isosceles

Text Solution

Verified by Experts

In triangle,`A B C`
let the altitude AD bisects `/_BAC`
Then we have to prove that the triangle ABC, is isosceles.
In `/_\`s ADB and ADC`
`/_BAD=/_CAD`
(AD is bisector of`/_BAC)`
`AD=AD`(common)
`/_ADB=/_ADC` (Each equal to 90)
`=>/_\ADB~=/_\ADC` (by ASA congruence criterion)
`AB=AC`(cpct)
Hence, A triangle `A B C`is an isosceles.
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