Question

In the adjoining figure 3, AD is the bisector of
the exterior angle A of triangle ABC. Seg AD intersects the
side BC produced in D. Prove that BD/C D=AB/AC​

Answer 1

Answer:

Construction : draw line EC parallel to AD

Proof: as EC is parallel to AD

By B. P. T

BE/AE=BC/CD

ANGLE KAD = angle AEC........ Corresponding angle test

angle DAC = angle ACE...........alternate angle test

Angle KAD= angle DAC....... given

Therefore,

angle AEC = angle ACE

triangle AEC is isoscleles triangle

By isoscleles triangle thm

AE=AC

BY COMPONENDO

BE+AE/AE=BC+CD/CD

AB/AE=BD/CD

AB/AC=BD/CD

HENCE PROVED