Solve Question:Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Question

Philoid · Accepted Answer

WE HAVE TO PROVE

In Δ ABC ray AD is an angle bisector.

Draw an parallel line to AD from C and extend the BA name the meeting point as E.

Now, AD ∥ to CE

If CB is a transversal to parallel line AD & CE

Then, ∠BAD ≡ ∠AEC (by Converse alternate angle test)

If AC is a transversal to parallel line AD & CE

∠CAD ≡ ∠ACE

∵ AD is an angle bisector

∠CAD ≡ ∠BAD

Now, in Δ AEC

From 1 & 2 relations we can say that

∠CAD ≡ ∠ACE

If base angles are congruent then segment AC ≡ segment AE

In Δ EBC,

Segment AD ∥ segment CE

∵ AC = AE

⇒

Solve Question:
Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.