In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle 's side is divided into by a line that bisects the opposite angle.

The triangle angle bisector theorem states that "The bisector of any angle inside a triangle divides the opposite side into two parts proportional to the other two sides of the triangle which contain the angle."

Thus, AP is the angle bisector of angle A, making our answer 0.

The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

The Angle Bisector Theorem states that when an angle in a triangle is split into two equal angles, it divides the opposite side into two parts. The ratio of these parts will be the same as the ratio of the …

Nov 16, 2025 · Let $\triangle ABC$ be a triangle. Let $D$ lie on the base $BC$ of $\triangle ABC$. Then the following are equivalent: where $BD : DC$ denotes the ratio between the lengths $BD$ and …

May 17, 2025 · In this guide, we have taken a deep dive into the trigonometric angle bisector theorem, exploring its derivation, practical applications, and potential pitfalls in a structured and accessible way.

Mar 26, 2016 · The Angle-Bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides. The following …

Jul 23, 2025 · Angle bisector theorem states that the angle bisector of a triangle divides the opposite side of a triangle into two parts such that they are proportional to the other two sides of the triangle.

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.