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The Angle Bisector

Part of the Angles section of Coddy's Geometry journey. Lesson 24 of 59.

A ray that cuts an angle into two equal halves is its bisector. The figure says so with matching arcs on the two halves: the ray BD bisects ∠ABC when ∠ABD and ∠DBC are equal.

$An 84 degree angle cut by its bisector into two halves of 42 degrees$

Since the halves are equal and together make the whole, the whole is twice either half: 84° splits into 42° and 42°. Going the other way, a half of 35° means the whole is 70°.

The rule on the board is Angle bisector: whole = 2 × half. Tap a half or the whole and pick it.

Challenge

The ray BD bisects ∠ABC, which measures 118°. Find ∠ABD, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Angles

1Meet the Angle

Your First Angle Angles on a Line Degrees and the Full Turn Across the Crossing

4Vertical Angles

Two Lines Cross Vertical Angles Are Equal Solving with Verticals All Four Angles Recap: At the Crossing

7Parallels and Transversals

Parallel Lines Corresponding Angles Alternate Angles Co-interior Angles Which Rule Is It Recap: The Three Pairs

10Isosceles and Equilateral

Base Angles Are Equal Finding the Apex Which Angles Match Equilateral Angles Isosceles at Work Recap: Twin Corners

2Naming and Equations

Adding Adjacent Angles Write the Equation Recap: Along the Line

5Around a Point

Angles Around a Point The Missing Angle Equal Slices Four Angles, One Point Recap: The Full Turn

8Angle Chases

Verticals Meet Parallels Is There Enough?From Figure to Equation Both Angles Labeled Recap: Through the Strip

11The Exterior Angle

The Exterior Angle Using the Shortcut Two Roads, One Answer Exterior in the Wild Recap: Outside View

3Right Angles and Complements

The Square Mark Complementary Angles Perpendicular Lines Finding the Complement Equal Parts of a Corner Recap: The Right Corner

6The Angle Bisector

The Angle BisectorBisected Expressions Bisecting a Straight Angle Recap: Split in Half

9Triangle Angle Sum

The 180 Rule Finding the Third Angle Two Unknown Angles Right Triangles Recap: The Budget

12Final Challenges

Final: The Angle Chase Final: Triangle Meets Line Final: The Full Round Final: Isosceles Chase Final: Master of Angles