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Question
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosce
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Solution
Given that the bisector of the exterior vertical angle of a triangle is parallel to the base and we have to prove that the triangle is isosceles
Let ABC be a triangle such that AD is the angular bisector of exterior vertical angle EAC and AD || BC
Let∠EAD = (1), ∠DAC = (2), ∠ABC = (3) and∠ACB = (4)
(1) = (2) [ ∵ AD is bisector of , ∠EAC ]
(1)=(3) [Corresponding angles]
and (2) = (4) [alternative angle]
⇒ (3) = (4) ⇒AB = AC
Since, in ΔABC, two sides AB and AC are equal we can say that
DABC is isosceles
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