Perpendicular Bisector Theorem

Learning Objectives Define a perpendicular bisector and its properties. State and explain the Perpendicular Bisector Theorem. State and explain the Converse of the Perpendicular Bisector Theorem. Apply the theorem and its converse to solve for unknown lengths and variables in geometric figures. Prove the Perpendicular Bisector Theorem using triangle congruence postulates. Determine if a point lies on a perpendicular bisector by applying the converse of the theorem. Imagine you and a friend are standing in a field. Where could a third person stand so they are the exact same distance from both of you? 🤔 This tutorial explores the Perpendicular Bisector Theorem, a fundamental rule in geometry that connects points, distances, and lines. You will learn the theorem, its converse...

TermDefinitionExample Perpendicular BisectorA line, ray, or segment that intersects another segment at its midpoint and forms a 90° angle.If line 'l' passes through the midpoint M of segment AB and l ⊥ AB, then 'l' is the perpendicular bisector of AB. EquidistantBeing at an equal distance from two or more points.If the distance from point C to point A is 5 cm, and the distance from point C to point B is also 5 cm, then C is equidistant from A and B. MidpointThe point on a line segment that divides it into two congruent (equal length) segments.If M is the midpoint of segment XY, then XM = MY. Perpendicular LinesTwo lines that intersect to form a right angle (90°).The x-axis and y-axis on a Cartesian plane are perpendicular lines. Congruent SegmentsLine segments that hav...

Perpendicular Bisector Theorem If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Use this theorem when you are GIVEN that a line is a perpendicular bisector and you need to prove or find the lengths of the segments connecting a point on that line to the endpoints. If line 'l' is the perpendicular bisector of segment AB and point P is on 'l', then PA = PB. Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment. Use this theorem when you are GIVEN that a point is equidistant from a segment's endpoints and you need to prove that the point lies on the perpendicular bisector. If PA...