Question

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Answer 1

AE is the bisector of the exterior angle ∠DAC of the Δ ABC and AE || BC

Now,

AB || BC {given}

∠1 = ∠2 {given}

So, ∠B = ∠1 {Corresponding angle}

and ∠C = ∠2 {Alternate angle}

=> ∠B = ∠C

=> AB = AC

So, Δ ABC is an isosceles triangle.

Answer 2

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From the figure,

AE is the bisector of the exterior angle ∠DAC of the Δ ABC and AE || BC

Now,

AB || BC {given}

∠1 = ∠2 {given}

So, ∠B = ∠1 {Corresponding angle}

and ∠C = ∠2 {Alternate angle}

=> ∠B = ∠C

=> AB = AC

So, Δ ABC is an isosceles triangle.

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