Question

Prove that the bisector of an angle the side opposite to the congle in the ratio of the remaining sides.​

Answer 1

Proof : Line CE∥ Line DA (Construction) and line BE is the transversal

∠BAD=∠AEC [Corresponding angles] ....(1)

AD∥EC

△AC is transversal

∴∠DAC=∠ACE [Alternative angles] ...(2)

But ∠BAD=∠DAC [Given] ...(3)

△∠AEC=∠ACE [from (1),(2) and (3)]

In △AEC side AC=side AE [Isosceles theorem] ...(4)$

Now in △BCE,segAD∥segCE

DC

BD

=

AE

AB

∴

DC

BD

=

AC

AB

Hence in a triangle, the angle bisector divides the side opposite to the angle in the ratio of the remaining sides.

Answer 2

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