Bisecting an Angle
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 44 of 61.
An angle bisector cuts an angle into two equal angles. It is built from a kite, a shape that folds onto itself.
To bisect the angle at V: draw a circle about V. It crosses the arms at X and Y, so VX = VY. Then draw a circle about X through Y and a circle about Y through X; they cross at Z, so XZ = YZ. Now VXZY is a kite: two pairs of equal sides. V and Z are both equally far from X and Y, so the line VZ is the perpendicular bisector of XY. It is the fold line of the kite, and the fold lands one half of the angle on the other.
Challenge
Construct the bisector of ∠ABC, the line that cuts it into two equal angles, then press Check.
Try it yourself
Construct it with a compass and straightedge
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Transformations & Constructions
7Drawing on Squared Paper
Lengths by PythagorasPerpendicular StepsSquares by AreaRight Triangles by AreaMidpoints on the GridRecap: Squared Paper10Perpendiculars and Parallels
Perpendicular From a PointPerpendicular at a PointParallel Through a PointTools You Have EarnedRecap: Parallels5Dilations
Scaling From a CenterShrinking a ShapeDilating About a PointNegative Scale FactorsRecap: Dilations8Compass and Straightedge
Circles Keep DistancesWhy the Sides MatchAngles You BuiltA 60° AngleRecap: Equilateral Triangle