Question

AD is median to the base BC of an isoceles triangle ABC in which AB =AC show that AD is bisector of angle A ( that is angle BAD =angle CAD )

Answer 1

AD is median of triangle ABC , so,
       BD = CD
       consider triangles ABD and ACD
               AB = AC (given)
             angleABD = angleACD (as AB = AC, angles opp to equal sides )
               BD = CD (fro above)
           so , from SAS congruence criteria, ABD=~ACD
                 so, angle BAD = angle CAD ( by cpct)
                               hence proved.

Answer 2

Answer:

ABC is an isosceles triangle since AB=AC. ∠B=∠C=35

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∠A=110

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(∵∠A+∠B+∠C=180

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)

In an isosceles triangle, median (AD) to the base BC is the angular bisector of ∠A

Hence, ∠BAD=55

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