Question

In the given figure, AB = AC and side BA has been produced
to D. If AE is the bisector of CAD, prove that AE || BC.
​

Answer 1

Answer:

Given : AB = AC , From base angle theorem we get ∠ ABC = ∠ ACB =x---( 1 )

And we know from external angle theorem :

∠ CAD = ∠ ABC + ∠ ACB , Substitute values from equation 1 we get

∠ CAD = x + x ,

∠ CAD = 2 x , Also given AE is bisector of ∠ CAD , So

∠ DAE = ∠ CAE = x ---( 2 )

From equation 1 and 2 we get∠ DAE = ∠ ABC and these are corresponding angles , we take BD as transversal line and that can only be true if

BC | | AE

( Hence proved )

( Hence proved )Hope this information will clear your doubts about topic.

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Answer 2

See the image for the answer

sorry at last there will be AE || BC