"Angle bisector theorem proof" is the topic often searched by almost all the students who study geometry in school level math.

Often students have this question in geometry. That is, " How to prove "Angle bisector theorem" ? ".

Even though students get answer for this question on internet, they do not understand exactly what has been explained.

To make the students to understand the proof of this theorem clearly, we have given step by step explanation.

Angle bisector theorem

The internal (external) bisector of an angle of a triangle divides the opposite side internally (externally) in the ratio of the corresponding sides containing the angle.

Proof (Internally) :

Proof (Externally) :

"Angle bisector theorem proof" is the much required stuff for the students who study Geometry in school level math. Even though students get proof of "Angle bisector theorem" on internet, they find it difficult to understand what has been explained.

Before students understand the proof of the theorem, first they are in the position to understand what the theorem says.

Once the theorem is understood by the students, they have to go through the proof step by step.

Always the topic "Geometry" in math is bit difficult for the students to understand. In order to make the topic "Geometry" as an easy one for the students, we have given step by step explanation for the proof of "Angle bisector theorem"

To understand this theorem, we have to go through the theorem along with the figure given above.

Theorem says, "The internal bisector of an angle of a triangle divides the opposite side internally in some ratio".

In the first figure , the above said work is done by the straight line, "AD".

Then, it says, "The ratio in which the line AD divides the side BC will be equal to the ratio of the sides AB and AC.

For example, if the line AD divides the side BC in the ratio 1:2, then the ratio of the two sides AB and AC will also be 1:2.

Here students may have a question. That is, how is this possible ?. That has been clearly explained in the step by step proof.

Please go through the the proof step by step.

When students go through the proof step by step, they will definitely be able to understand.