What are the undefined terms?

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Presentation transcript:

What are the undefined terms? Aim: What are the undefined terms? Do Now: What is a point? What is a line? 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. Geometry Leeson: Undefined Terms, Lines, Line Segments

Geometry Leeson: Undefined Terms, Lines, Line Segments

. P . A(2, 6) A point indicates a position or location in space. X Y . A(2, 6) Points are named using capital letters and/or coordinates. Geometry Leeson: Undefined Terms, Lines, Line Segments

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

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

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

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

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

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 of is 58 cm. If AB = x - 4, BC = 2x + 8, and CA= x – 2, what is BC? Ans. BC=36 cm Geometry Leeson: Undefined Terms, Lines, Line Segments

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

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

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

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

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