If ABC is an isosceles triangle with AB=AC and AD is an altitude, then

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Solution

In tringle ABD & ACD

AB=AC (GIVEN)

ANGLE ADB=ANGLE ADC(BOTH ARE RIGHT ANGLES)

AD=AD(COMMON)

SO BOTH THE TRIANGLES ARE CONGRUENT

THEREFORE BD=CD(CPCT)

ANGLE BAD=ANGLE CAD(CPCT)

HENCE AD BISECTS BOTH BC AND ANGLE A

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