Question

if the bisector of the exterior vertical angle of a triangle be parallel to the base show that the triangle is isosceles

Answer 1

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 :

AE Bisects Angle FAE equally as

FAE AND CAE WHICH ARE EQUAL.

ANGLE FAE =ANGLE ABC (CORRESPONDING ANGLES) -1

ANGLE EAC=ANGLE BCA (ALTERNATE ANGLES) -2

BY TAKING 1 AND 2 WE CAN SAY THAT

ANGLE ABC =ACB

SO AB =AC (ANGLES OPPOSITE TO THE EQUAL ANGLES ARE EQUAL)

HENCE WE VAN SAY THAT TRIANGLE ABC IS A ISOSCELES TRIANGLE.