Question

in triangle abc, ad is the bisector of angle A and AD BC show that triangle ABC is isosceles triangle

Answer 1

In ∆ ABD and ∆ ACD , we have

< ADB = < ADC = 90 ( given)

AD = AD ( common)

< BAD = < CAD ( AD bisects <A)

→ ∆ ABD congruent to ∆ ACD ( by AAS rule)

Thus, AB = AC ( by cpct)

Hence, ABC is an isosceles ∆.

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