Question

In ∆ABC, AE is the bisector of the exterior ∠CAD and AE || BC. Prove that AB = AC.

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Answer 1

Answer:

Since, AE∥BC,

thus, ∠EAC=∠ACB (Alternate angles)

Also, ∠DAE=∠EAC (AE bisects ∠ DAC)

∠DAC=∠ACB+∠ABC (Exterior angle is equal to sum of interior opposite angles)

∠ABC=∠DAC−∠ACB

or ∠ABC=∠DAC−∠EAC

∠ABC=∠DAE=∠EAC=∠ACB

Now, In △ABC

Since, ∠ABC=∠ACB

Hence, AB=AC (Opposite sides of equal opposite angles are equal)

Step-by-step explanation:

Answer 2

Answer:

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