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If the bisectors of exterior vertical angle of a triangle is parallel to the base, then prove that the triangle is isosceles.?
Verified Answer
If the bisectors of exterior vertical angle of a triangle is parallel ...

From the figure,

AE is the bisector of the exterior angle ∠DAC of the Δ ABC and AE || BC

Now,

AB || BC   {given}

∠1 = ∠2    {given}

So, ∠B = ∠1    {Corresponding angle}

and ∠C = ∠2    {Alternate angle}

=> ∠B = ∠C

=> AB = AC

So, Δ ABC is an isosceles triangle.
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If the bisectors of exterior vertical angle of a triangle is parallel ...
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If the bisectors of exterior vertical angle of a triangle is parallel to the base, then prove that the triangle is isosceles.?
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