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Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts in geometry do not have precise definitions but, we understand their meanings intuitively. We say these concepts are undefined. What are the undefined terms?

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Geometry Leeson: Undefined Terms, Lines, Line Segments 2

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3 A point indicates a position or location in space.. P X Y. A(2, 6) Point: Points are named using capital letters and/or coordinates.

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Geometry Leeson: Undefined Terms, Lines, Line Segments 4 A line is an infinite set of adjacent points. Line: Ex: Curved line Ex: Straight line Naming a Line: a)Two points on the line: b)Single lowercase letter ABC m

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Geometry Leeson: Undefined Terms, Lines, Line Segments 6 Plane: A plane is a set of points that forms a completely flat surface. Naming a Plane: a)Three points on the plane: b)Single uppercase letter: A C B Plane ABC R Plane R

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Intersections? Lines intersect at a point Planes intersect at a line

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Geometry Leeson: Undefined Terms, Lines, Line Segments 8 Def: Collinear Points: A collinear set of points is a set of points all of which lie on the same straight line. ABCD E Points A, B, C and D are collinear. Points A, E and C are not collinear.

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Geometry Leeson: Undefined Terms, Lines, Line Segments 9 Def: Line Segment: Naming a Line Segment: Use the names of the endpoints. AB Line segmentis part of Line A line segment is the set of two points on a line called endpoints, and all points on the line between the endpoints. AB

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Geometry Leeson: Undefined Terms, Lines, Line Segments 10 Measure of Line Segments: The measure of a line segment is the length of the line segment. To indicate the measure of a line segment, use the name of the line segment without the line above the name. Ex:= measure of line segment Ex: The perimeter ofis 58 cm. If AB = x - 4, BC = 2x + 8, and CA= x – 2, what is BC? Ans. BC=36 cm

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Geometry Leeson: Undefined Terms, Lines, Line Segments 11 Def: Congruent Line Segments: Congruent line segments are segments that are equal in measure. Then AB = CD Ans. CD = 29, AB = 29 Ex: A C D B If

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Geometry Leeson: Undefined Terms, Lines, Line Segments 12 Def: Midpoint The midpoint of a line segment divides the line segment into two congruent segments. AB M 1) 3) 5) 2) 4) 6)

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Geometry Leeson: Undefined Terms, Lines, Line Segments 13 Def: Line Bisector The bisector of a line segment is a line that intersects the line segment at its midpoint. AB M P Q 1) X 2)

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Geometry Leeson: Undefined Terms, Lines, Line Segments 14 Addition and Subtraction of Line Segments: R P S If several line segments belong to the same line, we can write addition and subtraction expressions using the names of these segments.

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Geometry Leeson: Undefined Terms, Lines, Line Segments 15 Simple 2-Column Proof Given Definition of Line Bisector Definition of Midpoint B A F E P

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