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Constructing Angle Bisectors: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Constructing Angle BisectorsConstructing Angle Bisectors: Definition and ExamplesTable of ContentsConstructing Angle Bisectors Definition of Angle Bisectors

An angle bisector is a line that divides a given angle into two equal parts. When two rays meet at a point called a vertex, they form an angle. The angle bisector is a line that goes through the vertex and splits the angle into two equal halves. For example, if an angle bisector is constructed for an angle of 808080 degrees, it divides the angle into two equal angles of 404040 degrees each.

Angle bisectors can be constructed for all types of angles, including acute angles, obtuse angles, and right angles. The tools needed for constructing an angle bisector include a ruler, pencil, compass, and protractor. There are two main methods for constructing angle bisectors: using a compass and using a protractor, each with its own set of steps and mathematical principles.

Examples of Constructing Angle Bisectors Example 1: Using an Angle Bisector to Compare Angles Problem:

Ray OMOMOM is an angle bisector of ∠AOB∠AOB∠AOB. If ∠AOM∠AOM∠AOM is 42∘42^\circ42∘, what is the measure of angle ∠MOB∠MOB∠MOB and ∠AOB∠AOB∠AOB?

Angle Bisector

Step-by-step solution:

Step 1, An angle bisector divides an angle into two equal parts.

Step 2, Since ray OMOMOM is an angle bisector, it means:

∠AOM=∠MOB\angle AOM = \angle MOB∠AOM=∠MOB

Step 3, The problem tells us ∠AOM∠AOM∠AOM is 42∘42^\circ42∘,

so: ∠MOB=42∘\angle MOB = 42^\circ∠MOB=42∘

Step 4, The total angle is:

∠AOB=∠AOM+∠MOB\angle AOB = \angle AOM + \angle MOB∠AOB=∠AOM+∠MOB =42∘+42∘= 42^\circ + 42^\circ=42∘+42∘ =84∘= 84^\circ=84∘

Step 5, Therefore, ∠MOB∠MOB∠MOB is 42∘42^\circ42∘, and ∠AOB∠AOB∠AOB is 84∘84^\circ84∘.

Example 2: Drawing an Angle Bisector with a Protractor Problem:

How can you draw the angle bisector of 50∘50^{\circ}50∘ with a protractor?

Step-by-step solution: Step 1, Draw a baseline ABABAB. Put the center of the protractor on the point AAA.

Drawing an Angle Bisector with a Protractor

Step 2, Now, we will mark two points using the inner calibration of the protractor.

First, mark a point CCC representing the 505050 degree angle. Next, mark a point DDD representing the 252525 degree angle since it is exactly half of 505050 degrees.

Step 3, Remove the protractor. Join points AAA and CCC. Join the points AAA and DDD.

Drawing an Angle Bisector with a Protractor

Step 4, ADADAD is the angle bisector of ∠BAC\angle BAC∠BAC. ∠BAD=∠CAD=12∠BAC=25∘\angle BAD = \angle CAD = \frac{1}{2} \angle BAC = 25^{\circ}∠BAD=∠CAD=21​∠BAC=25∘ ∠BAC=50∘\angle BAC = 50^\circ∠BAC=50∘ Example 3: Finding Missing Values Using Angle Bisector Properties Problem:

Find the value of xxx if OMOMOM is an angle bisector.

Angle Bisector

Step-by-step solution:

Step 1, Since OMOMOM is an angle bisector, the angles BOMBOMBOM and AOMAOMAOM are equal.

Step 2, Set up an equation based on the given angle measures:

2x+1=352x + 1 = 352x+1=35

Step 3, Solve for xxx by isolating the variable:

2x=342x = 342x=34 x=17x = 17x=17 Comments(2)FFloristOscarNovember 4, 2025I've used this page to teach angle bisectors. The clear def and examples made it easy for students to grasp. Great resource!

NNatureLover75September 17, 2025I’ve used the step-by-step guide to teach my kids how to construct angle bisectors—it’s super clear and easy to follow! The examples really helped them understand the concept better too.

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