Welcome to Geometry Ms. Urquhart

Identify Points, Lines, and Planes Lesson 1-1 Identify Points, Lines, and Planes Lesson 1-1 Point, Line, Plane

Points (Undefined term) 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 C A Lesson 1-1 Point, Line, Plane

Lines (Undefined Term) 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 Lesson 1-1 Point, Line, Plane

Lesson 1-1 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 are 2 dimensional 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 letter without a dot – Plane M (2) Any 3 non-collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA Link to movie on green plane A M B C Horizontal Plane Vertical Plane Other Lesson 1-1 Point, Line, Plane

Different planes in a figure: B Plane ABD Plane FGH Plane BCF Plane DHE Plane BEF Plane CDG 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 FGD Plane ACE Plane ACH Plane AGF Plane BDG Etc. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Coplanar Objects **Remember: Any 3 non-collinear points determine a plane! 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

Lesson 1-1 Point, Line, Plane Example 1 a. Give two other names for b. Give two other names for plane R c. Name three points that are collinear d. Name four points that are coplanar. Line n and QP plane VSP, plane SVT, plane PVT, etc. points S,P, and T Points T,V,S, and P or points S,P, T, and Q Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Segment a straight line which links 2 points without extending beyond them. The symbol for line segment AB is Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Rays B A have a beginning point but no end point.  Think of sun's rays: they start at sun and go on forever... Opposite Rays: 2 rays that lie on the same line, with a common endpoint and no other points in common.  How to Name? AB Opposite rays form a straight line and/or a straight angle (180°). AB and AC are opposite rays *When labeling: we always start with the endpoint first and the arrow points to the right. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane EXAMPLE 2 a. Give another name for . b. Name all rays with endpoint J. Which of these rays are opposite rays? 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 R and Plane P intersect at the line Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane GUIDED PRACTICE Use the diagram at the right. 5. Name the intersection of and line k. 6. Name the intersection of plane A and plane B. 7. Name the intersection of line k and plane A. Point M line k line k Lesson 1-1 Point, Line, Plane