Question

If the bisector of exterior vertical angle of a triangle is parallel to the base , show that the triangle is isosceles

Answer 1

Hey mate..
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∠CAE is the external vertical angle and AD is its bisector.

∴ ∠CAD = ∠DAE  ...... (i)

As, AD || BC

∴ ∠CAD = ∠ACB  ...... (ii)  (alternate angle)

and ∠DAE = ∠ABC  ......(iii)  (corresponding angle)

From (i), (ii) and (iii),

∠ABC = ∠ACB

∴ AC = AB  (opposite sides to equal angles)

Hence, ΔABC is isosceles.

Hope it helps !