The Equidistance Theorems Geometry Section 4.4 Students will recognize and use the relationship between equidistance and perpendicular bisectors.

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The EQUIDISTANCE Theorems

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Presentation transcript:

The Equidistance Theorems Geometry Section 4.4 Students will recognize and use the relationship between equidistance and perpendicular bisectors.

The Equidistance Theorems Geometry Section 4.4 Students will recognize and use the relationship between equidistance and perpendicular bisectors.

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. A XY C B D XY F E N X Y M

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. A XY C B D XY F E N X Y M

Example 1 StatementsReasons BD A C E

The Equidistance Theorems Geometry Section 4.4 Students will recognize and use the relationship between equidistance and perpendicular bisectors. Assignment Page 187 #1-4,6

The Equidistance Theorems Geometry Section 4.4 (Day 2) Students will recognize and use the relationship between equidistance and perpendicular bisectors.

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

Example 1 StatementsReasons K T E I X

Example 2 StatementsReasons BC A D E

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