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## Point, Line, Plane

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**Point, Line, Plane**Point, Line, Plane**Geometry Terms**• Undefined terms: words that do not have a formal definition but there is agreement about what they mean. • Defined terms: Terms that can be described using known words • Postulate or Axiom: Rule that is accepted without proof. • Theorem: Rule that can be proved. Point, Line, Plane**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 Point, Line, Plane**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 B C Point, Line, Plane**Collinear Points**• Collinear points are points that lie on the same line. (The line does not have to be visible.) • A point lies on the line if the coordinates of the point satisfy the equation of the line. Ex: To find if A (1, 0) is collinear with the points on the line y = -3x + 3. Substitute x = 1 and y = 0 in the equation. 0 = -3 (1) + 3 0 = -3 + 3 0 = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. A B C Collinear C A B Non collinear Lesson 1-1 Point, Line, Plane**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 Lesson 1-1 Point, Line, Plane**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 Lesson 1-1 Point, Line, Plane**Other planes in the same figure:**Any three non collinear points determine a plane! Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc. Lesson 1-1 Point, Line, Plane**Coplanar Objects**Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No Lesson 1-1 Point, Line, Plane**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……. Lesson 1-1 Point, Line, Plane**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 Lesson 1-1 Point, Line, Plane**RA : RA and all points Y such that**A is between R and Y. ( the symbol RA is read as “ray RA” ) Ray Definition: How to sketch: How to name: Lesson 1-2: Segments and Rays**Opposite Rays**Definition: If A is between X and Y, AX and AY are opposite rays. ( Opposite rays must have the same “endpoint” ) opposite rays not opposite rays Lesson 1-2: Segments and Rays**Segment**Part of a line that consists of two points called the endpoints and all points between them. Definition: How to sketch: How to name: AB (without a symbol) means the length of the segment or the distance between points A and B. Lesson 1-2: Segments and Rays**12**AC + CB = AB x + 2x = 12 3x = 12 x = 4 The Segment Addition Postulate Postulate: If C is between A and B, then AC + CB = AB. If AC = x , CB = 2x and AB = 12, then, find x, AC and CB. Example: 2x x Step 1: Draw a figure Step 2: Label fig. with given info. Step 3: Write an equation x = 4 AC = 4 CB = 8 Step 4: Solve and find all the answers Lesson 1-2: Segments and Rays**Homework**• Pg. 5 # 1 • Pg 6 # 17, 18, 20 • Pg 12 # 8, 10, 12 • Pg 13 #21 to 26, 29 Lesson 1-2: Formulas