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Question
In the given figure; AE bisects exterior angle CAD and AE is parallel to BC.
Prove that : AB = AC.
In the given figure; AE bisects exterior angle CAD and AE is parallel to BC.
Prove that : AB = AC.
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Solution
Since AE || BC and DAB is the transversal
∠ DAE=∠ABC = ∠B
Since AE || BC and AC is the transversal
∠CAE=∠ABC = ∠C
But AE bisects ∠CAD
∠ DAE = ∠CAE
∠B = ∠C
AB = AC[Sides opposite to equal angles are equal]
Since AE || BC and DAB is the transversal
∠ DAE=∠ABC = ∠B
Since AE || BC and AC is the transversal
∠CAE=∠ABC = ∠C
But AE bisects ∠CAD
∠ DAE = ∠CAE
∠B = ∠C
AB = AC[Sides opposite to equal angles are equal]
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