The Perpendicular Bisector
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 42 of 61.
The perpendicular bisector of a segment crosses it at its midpoint, at right angles. Every point on it is the same distance from both ends, and every point that is equally far from both ends lies on it.
To build it for XY: draw the circle about X through Y and the circle about Y through X. They cross at U and V, and the line UV is the perpendicular bisector. Why? U is XY from X and XY from Y, so it is equally far from both ends, and so is V. Better still, XUYV has four sides all equal to XY: it is a rhombus, and the diagonals of a rhombus cut each other in half at right angles.
Challenge
Construct the perpendicular bisector of AB, 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