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## 1.1 Identify Points, Lines, and Planes

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**1.1 Identify Points, Lines, and Planes**Goal Name & Sketch Geometric Figures**A point has no dimension. It is represented by a small dot.**Point A A A line has one dimension. It extends without end in two directions. It is represented by a line with two arrowheads. ℓ Line ℓ or BC B C**Lines**• Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: 2 ways (1) small script letter – line n (2) any two points on the line - • Never name a line using three points - n A C**Points**• Points do not have actual size. • How to Sketch: Using dots • How to label: Use capital letters Never name two points with the same letter (in the same sketch). A B A C**Collinear Points**• Collinear points are points that lie on the same line. (The line does not have to be visible.) A B C Collinear Non collinear A C B**F**D E A plane has two dimensions. It is represented by a shape that looks like a floor or wall. You have to imagine that it extends without end. plane M or plane DEF M**Planes**• A plane is a flat surface that extends indefinitely in all directions. • How to sketch: Use a parallelogram (four sided figure) • How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C Horizontal Plane Vertical Plane Other**Different planes in a figure:**A B Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. D C E F H G**Other planes in the same figure:**Any three non collinear points determine a plane! Plane AFGD Plane ACGE Plane ACH Etc.**Coplanar objects (points, lines, etc.) are objects that lie**on the same plane. The plane does not have to be visible. Coplanar Objects Are the following points coplanar? A, B, C ? Yes No A, B, C, F ? H, G, F, E ? Yes E, H, C, B ? Yes Yes A, G, F ? C, B, F, H ? No**Postulates are statements that are accepted without further**justification or proof. Postulates (write this down) Postulate, Two points determine a line. Through any two points there is exactly one line. Postulate, Three points determine a plane. Through any three points not on a line there is exactly one plane.**Example**1 Use the diagram at the right. p a. Name three points. D E b. Name two lines. c. Name two planes. m F Q R Name Points, Lines & Planes**Collinear points are points that lie on the same line**Coplanar points are points that lie on the same plane. Coplanar lines are lines that lie on the same plane.**Example**2 Collinear & Coplanar Points Use the diagram at the right. H a. Name three points that are collinear. F E D b. Name four points that are coplanar. G c. Name three points that are not collinear.**endpoint**endpoint The segment AB consists of the endpoints A and B, and all points on AB that are between A and B. A B Please understand that AB is the same as BA and that AB is the same as BA**endpoint**The ray AB consists of the endpoint A and all points on AB that lie on the same side of A as B. A B Understand that AB is NOT the same as BA**2. Draw JK.**3. Draw KL. 4. Draw LJ. K J L Example 3 Draw Lines, Segments, & Rays Draw three noncollinear points, J, K, and L. Then draw JK, KL, and LJ. 1. Draw J, K, and L.**Intersection of Figures**The intersection of two figures is the set of points that are common in both figures. The intersection of two lines is a point. m Line m and line n intersect at point P. P n Continued…….**3 Possibilities of Intersection of a Line and a Plane**(1) Line passes through plane – intersection is a point. (2) Line lies on the plane - intersection is a line. (3) Line is parallel to the plane - no common points. Lesson 1-1 Point, Line, Plane**Intersection of Two Planes is a Line.**B P A R Plane P and Plane R intersect at the line end