Question

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


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Answer 1

Step-by-step explanation:

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)