In ∆ABC, AE is the bisector of the exterior ∠CAD and AE || BC. Prove that AB = AC.
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In ∆ABC, AE is the bisector of the exterior ∠CAD and AE || BC. Prove that AB = AC.
i am very sad bye take care
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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:
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Answer:
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