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Question

In given figure AD is an altitude of an isosceles triangle ABC in which AB=AC.
Show that, AD bisects A
569836_3f97a4589abf4c149e9d907aa009330b.png

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Solution

As ABC is an isosceles triangle, AB=AC

AD is the altitude, ADC=ADB=90o

In ADB and ADC,

ADC=ADB=90o

AB=AC and AD=AD [common]

ADBADC [RHS Congruency]

Hence by CPCT,

BD=DC

BAD=DAC

i.e, AD bisects A [henceproved]

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