Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

If then .

Example:

is an angle bisector. Find the value of x.

Solution:

is an angle bisector. Therefore, by the Angle Bisector Theorem, BC = BD.

Substitute the lengths of BC and BD.

3x + 3 = x + 7

Subtract 3 from each side.

3x = x + 4

Subtract x from each side.

2x = 4

Divide both sides by 2.

The value of x is 2.