Undefined Terms • In geometry, some words are undefined. • Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry. • A point indicates a location and has no size. • Usually represented by a dot and named with a capital letter.
Undefined Terms, con’t • A line is a straight path that extends in two opposite directions without end. • Usually represent by a straight line with arrow heads on each end and named by one lowercase letter or two capital letters, such as . • A plane is represented by a flat surface that extends without end in all directions. • Usually represented by a quadrilateral and named by one capital letter or three points that lie on it.
Collinear and Coplanar • Points that lie on the same line are collinear points. • Points and lines that lie in the same plane are coplanar. • All the points of a line are coplanar!
Naming Points, Lines and Planes • What are two other ways to name ? • What are two other ways to name plane P? • What are the names of three collinear points? • What are the names of four coplanar points?
Defined Terms • A segment is part of a line that consists of two endpoints and all points between them. • Segments are named by their endpoints. • A ray is part of a line that consists of one endpoint and continues in the other direction. • Rays are named by their endpoint and another point on the ray (the order of the points indicates the direction of the ray!).
Defined Terms, con’t • Opposite rays are two rays that share the same endpoint and form a line. • How would you name the opposite rays above?
Naming Segments and Rays • What are the names of the segments in the figure? • What are the names of the rays? • Which of the rays are opposite rays?
Postulates • A postulate is an accepted statement of fact. • Postulates cannot be proven! Postulate 1-1 : Through any two points there is exactly one line.
Intersection • When you have two or more figures, their intersection is the set of points the figures have in common. Postulate 1-2: If two distinct lines intersect, then they intersect in exactly one point. Postulate 1-3: If two distinct planes intersection, then they intersect in exactly one line.
Finding the Intersection of Two Planes • Each surface of the box below represents part of a plane. • What is the intersection of plane ADC and plane BFG? *NOTE: When naming a plane, list corner points in consecutive order!
Noncollinear Points • Points which do not lie on the same line are noncollinear. • Three or more points are noncollinear if they are not ALL on the same line! Postulate 1-4: Through any three noncollinear points there is exactly one plane.
Using Postulate 1-4 • What plane contains points N, P, and Q? Shade the plane. • What plane contains points J, M, and Q? Shade the plane.