Question

1. AP is the bisector of angle CAD and AP parellel BC:
prove that AB =AC
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Answer 1

Since AP||BC

So, angle DAP = angle ABC ... (1)

( corresponging angle)

Also, angle PAC = angle ACB.... (2)

( alternate interior angles)

But, angle DAP = angle PAC ( AP bisects DAC)

from (1) and (2), we get,

angle ABC = angle ACB

So, AB = AC ( sides opposite to equal angles are equal)