ABC is an isosceles triangle with AB=AC and D is a point on ABC BC such that `AD_|_BC` (see figure ). To prove that `angleBAD =angleCAD ` a student proceeded as follows

`In Delta ABD and Delta ACD`,we have
` AB=AC " " [" Given"]`
`angleB=angleC " "[because` AB=AC ]
`and " "angleADB= angleADC `
Therefore` " " DeltaABD cong Delta ACD " " ["by AAS congruence rule"]`
So , ` " "angleBAD =angleCAD " " [by CPCT]`
What is the defect in the above argument ?