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Angle Bisector

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Angle Bisector

Study Guide

Key Definition

An angle bisector is a line or ray that divides an angle into two congruent angles. If $\overrightarrow{KM}$ bisects the angle $\angle JKL$, then the angles $\angle JKM$ and $\angle LKM$ are congruent.

Important Notes

Any point on the angle bisector is equidistant from the two sides of the angle.
The Angle Bisector Theorem supports the Incenter Theorem, which states that the intersection of all three angle bisectors in a triangle is the incenter – the point equidistant from all three sides.

Mathematical Notation

$\overrightarrow{KM}$ represents a ray in the direction of K to M.

$\angle JKL$ represents the angle formed by the points J, K, and L.

Remember to use proper notation when solving problems

Why It Works

By the Angle Addition Postulate, the two angles formed by the bisecting ray add up to the original angle’s measure. Since these angles are congruent, each must be exactly half of the original angle.

Remember

The crucial point to remember is that an angle bisector divides an angle into two equal parts.

Quick Reference

Angle Bisector:A line or ray that divides an angle into two congruent angles.

Understanding Angle Bisector

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

An angle bisector is simply a line or ray that splits an angle into two equal parts.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If $\overrightarrow{BD}$ is an angle bisector of $\angle ABC$, and $m \angle CBD = 65\degree$, find $m \angle ABC$.

Real-World Problem

Question Exercise

Intermediate

Architectural Scenario

As an architect, you are designing a new building. You want to create a unique window design where a ray bisects an angle, creating two congruent angles. If one of the congruent angles measures 40\degree, how would you calculate the total angle?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider a scenario where a ray bisects an angle, creating two congruent angles. If you know the measure of the total angle is 120\degree, how would you find the measure of each individual angle?

Recap

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Review key concepts and takeaways