The Equidistance Theorems Geometry Section 4 4 Students

The Equidistance Theorems Geometry Section 4. 4 Students will recognize and use the relationship between equidistance and perpendicular bisectors. Developed by Cary Hill ~ North Junior High, Boise

Introduction Definition: The distance between two objects is the length of the shortest path between them. Postulate: A line segment is the shortest distance between two points. Definition: Equidistant means two points are the same distance from some other object. Definition: The perpendicular bisector ( bis. ) of a segment is the line that bisects and is perpendicular to the segment.

Theorems of the Day Theorem 24: If two points are each equidistant from the endpoints of a segment, then the points determine the perpendicular bisector. D A X E N Y B X X C Y F M Y

Theorems of the Day Theorem 25: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment. D A X E N Y B X X C Y F M Y

A Example 1 B E C Statements Reasons D

Theorems Review Theorem 24: 2 pts =dist from endpts of seg bis T H S A N Theorem 25: Pt on bis =dist from endpts of seg C A R Y H

Example 1 I T X E K Statements Reasons

A Example 2 E B Statements D Reasons C

The Equidistance Theorems Geometry Section 4. 4 Students will recognize and use the relationship between equidistance and perpendicular bisectors. Assignment Page 187 #9, 12, 14, 16, 17, 20