If D is any point on the base B C produc...

If `D` is any point on the base `B C` produced, of an isosceles triangle `A B C` , prove that `A D > A Bdot`

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In `/_\ABC`
we have` AB = AC`
`/_ABC = /_ACB` .....(1)
[ since Angle opp. to equal sides are equal]
In `/_\ABD`
we have Ext`/_ABC > /_ADB`
this implies`/_ABC > /_ADB`.....(2)From (1) and (2), we get`/_ACB>/_ADB`
` /_ACD>/_ADC`
[ since` /_ACB=/_ACD`,`/_ADB=/_ADC`]
this implies `AD > AC`
[since side opp. to greater angle is larger]
this implies `AD > AB` [since `AB = AC`]

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