Mathematics
In △ABC, D is a point on BC such that AD is the bisector of ∠BAC. CE is drawn parallel to DA to meet BD produced at E. Prove that △CAE is isosceles.
Triangles
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Answer
From figure,
∠DAC= ∠ACE (Alternate angles)
∠BAD = ∠CEA (Corresponding angles)
But, ∠BAD = ∠DAC (as AD is bisector of ∠BAC)
∴ ∠ACE = ∠CEA
AE = AC (Sides opposite to equal angles are equal.)
∴ △CAE is isosceles triangle.
Hence, proved that △CAE is isosceles triangle.
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