Pre-AP Bellwork • Describe what the slope of the line is and how you can calculate it. Use complete sentences.
Pre-AP Bellwork 2) Sketch the a figure for the given information. Then state the postulate that the figure illustrates a. AB and EF intersect in point C b. Planes LNP and MVK intersect in NM.
Pre-AP Bellwork 3) If one ray contains another ray, are they the same ray? Explain.
1-2 Points, Lines and Planes Geometry
Geometry is a mathematical system built on accepted facts, basic terms, and definitions. • Words like point,line, and plane are undefined terms. • They are the basic ideas that are used to build all other definitions in geometry.
A point indicates a location and has no size. It is usually represented by a small dot. It is named by a capital letter. A Point A
l A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. A line contains infinitely many points A Collinear Points – Points that lie on the same line B Line l or AB Points A,B,C are collinear points C
A M C B -You must imagine that the plane extends without end even though the drawing of a plane appears to have edges. A plane extends in two dimensions. It is a flat surface with no thickness. -A plane is named by a single capital letter or by at least three of its noncollinear points. Plane M or plane ABC
A M C B Points and lines in the same plane. Coplanar Points Plane M or plane ABC
A few basic concepts . . . • Must be commonly understood without being defined. One such concept is the idea that a point lies on a line or a plane. • Collinear points are points that lie on the same line. • Coplanar points are points that lie on the same plane.
Ex. 1: Naming Collinear and Coplanar Points H G • Name three points that are collinear Solution: D, E and F lie on the same line, so they are collinear. E F D
Ex. 1: Naming Collinear and Coplanar Points H G • Name four points that are coplanar. Solution: D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn. E F D
Ex. 1: Naming Collinear and Coplanar Points H G • Name three points that are not collinear. Solution: There are many correct answers. For instance, points H, E, and G do not lie on the same line. E F D
A B Segment AB l B • line segment- part of a line that consists of two endpoints and all the points between them. • symbolized by AB or BA. A Line l or AB
A B Ray AB l B • Ray- Part of a line that consists of one endpoint and all the points of the line on one side of the endpoint. • The ray AB (symbolized by AB). Note- The endpoint of the ray must be the first letter. A Line l or AB
More . . . l B • If C is between A and B, then CA and CB are opposite rays. • Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane. C A Line l or AB
OYO l C • What are the names of the segments in the figure at the right? • What are the names of the rays in the figures. • What rays in part(2) are opposite rays? B A
Postulate or axiom- an accepted statement of fact t B Postulate 1-1 Through any two points there is exactly one line Line t passes through points A and B. Line t is the only line that passes through these points A Line t or AB
t D B Postulate 1-2 If two distinct lines intersect they intersect exactly at one point AE and DB intersect in point C. C E A
Postulate 1-3 If two distinct planes intersect they intersect in exactly one line Plane A and Plane B intersect in CD.
Postulate 1-4 G Through any three noncollinear points there is exactly one plane. Points G,D, and E are noncollinear. Plane F is the only plane that contains them. F E D