Question

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

Answer 1

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.

Answer 2

Answer:

Given, <1=<2

AE || BC

<1=<4(corresponding angles )

<2=<3(alternate interior angles )

To prove:-AB= AC

<1=<4

<2=<3

<1=<2=<4=<3

<3=<4.

So, AB = AC