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Angle Bisector: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Angle BisectorAngle Bisector: Definition and ExamplesTable of ContentsAngle Bisector: Definition, Properties, and Construction Definition of Angle Bisector

An angle bisector is a ray or line segment that divides an angle into two equal parts. The term "bisector" means division into two equal parts. When an angle is bisected, it creates two angles of equal measure. For example, an angle bisector of a 60∘60^\circ60∘ angle will divide it into two angles of 30∘30^\circ30∘ each, forming two congruent angles.

Angle bisectors play important roles in triangles. Every triangle has three angle bisectors—one from each vertex. The point where these three angle bisectors meet is called the "incenter," which is equidistant from all sides of the triangle. An important property of angle bisectors is that any point on an angle bisector is at equal distances from the sides of the angle. Additionally, the angle bisector in a triangle divides the opposite side in a ratio equal to the ratio of the other two sides.

Examples of Angle Bisector Example 1: Finding the Measure of Angles Created by an Angle Bisector Problem:

An angle bisector divides an angle of 80∘80^\circ80∘. What will be the measure of each angle?

Step-by-step solution: Step 1, Recall what an angle bisector does. An angle bisector divides an angle into two equal parts. Step 2, Find each angle measure by dividing the original angle measure by 222. 80∘÷2=40∘80^\circ \div 2 = 40^\circ80∘÷2=40∘ Step 3, Confirm the result. Each angle will measure 40∘40^\circ40∘, and together they make up the original 80∘80^\circ80∘ angle. Example 2: Using the Angle Bisector Property to Find Unknown Values Problem:

For the image given below, find xxx if the ray OMOMOM is an angle bisector.

Angle Bisector

Step-by-step solution: Step 1, Write what we know. Since OMOMOM is an angle bisector, we know that m∠AOM=m∠MOBm\angle AOM = m\angle MOBm∠AOM=m∠MOB. Step 2, Look at the angle measures. The angles are given as 4x+54x + 54x+5 and 373737. Step 3, Set up an equation because the angles must be equal. 4x+5=374x + 5 = 374x+5=37 Step 4, Solve for xxx. 4x=37−54x = 37 - 54x=37−5 4x=324x = 324x=32 x=324x = \frac{32}{4}x=432​ x=8x = 8x=8 Example 3: Applying the Angle Bisector Theorem Problem:

For the image given below, determine the value of xxx, if BSBSBS is an angle bisector.

Angle Bisector

Step-by-step solution: Step 1, Understand the angle bisector theorem. If BSBSBS is the angle bisector of ∠ABC\angle ABC∠ABC, then ABBC=ASCS\frac{AB}{BC} = \frac{AS}{CS}BCAB​=CSAS​. Step 2, Substitute the known values from the diagram. AB=18AB = 18AB=18, BC=24BC = 24BC=24, AS=12AS = 12AS=12, and CS=xCS = xCS=x. Step 3, Set up the proportion. ABBC=ASCS\frac{AB}{BC} = \frac{AS}{CS}BCAB​=CSAS​ 1824=12x\frac{18}{24} = \frac{12}{x}2418​=x12​ Step 4, Solve for xxx using cross multiplication. 18×x=24×1218 \times x = 24 \times 1218×x=24×12 18x=28818x = 28818x=288 x=28818x = \frac{288}{18}x=18288​ x=16x = 16x=16 Comments(3)PPhotographyEnthusiastAveryNovember 5, 2025I've used this angle bisector def. with my students. It's clear & helped them grasp the concept. Great resource for geometry learning!

TTranslatorIrisNovember 4, 2025I've used this angle bisector def for my kid's study. It's clear & helped them grasp the concept easily. Great resource!

NNatureExplorerSeptember 17, 2025This explanation of angle bisectors was super clear! I used it to help my son with his geometry homework, and the examples made it so much easier for him to understand. Thanks for breaking it down!

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