Question 128
If the external bisector of the vertical angle $$\angle$$ A of the $$\triangle$$ ABC is parallel to the base BC, then the $$\triangle$$ ABC is a/an
Solution
AE is the bisector of the exterior $$\angle$$ DAC of the $$\triangle$$ ABC and AE || BC
Now, $$\angle$$ $$1$$ = $$\angle$$ $$2$$ (given)
Also, $$\angle$$ $$B$$ = $$\angle$$ $$1$$ (Corresponding angle)
and $$\angle$$ $$C$$ = $$\angle$$ $$2$$ (Alternate angle)
=> $$\angle$$ $$B$$ = $$\angle$$ $$C$$
=> AB = AC
So, $$\triangle$$ ABC is an isosceles triangle.
=> Ans - (B)
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