Question

In triangle ABC, the bisector AD of angle A is perpendicular to angle BC. Show that AB=AC& triangle ABC is isosceles

Answer 1

here is the solution...
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Answer 2

$in \: ∆abd \: and \: ∆acd.. \\ < bad \: = \: < cad \: \: \: \: \: \: \: (given)$

$ad \: = ad \: \: \: \: \: (common)$

$< adb = \: < adc \: = {90}^{o} \: \: (given)$

So , ∆ABD ≈ ∆ACD. (ASA rule)

So,. AB = AC. (CPCT)

or, ∆ABC is an Isoceles Triangle

Hence Proved