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Points, Lines and Planes Overview What you should already know! What you should learn! • Point - no size, location; represented by a small dot and named by a capital letter; A. • A geometric figure is a set of points. • Space is the set of all points. S X A C B Q • Line - series of points that extends in two opposite directions. Name with two points, AB, or a lower case letter, l. A B l •Points that lie on the same line are collinear. •Name 3 collinear points. •Name 3 non-collinear points. Plane - flat surface that extends in all directions; it has no thickness. Name a plane with a single capital letter, P, or name at least 3 non-collinear points in the plane. Points and lines in the same plane are coplanar. 1. Name this plane in two ways. 2. Can plane Q be called plane ABF? plane ABD? 3. Are the following points collinear? A, B, C E, B, C 4. Are the following sets of points coplanar? Plane Q and line BF line AB and line ED Euclid of Alexandria Born: about 325 BC Died: about 265 BC in Alexandria, Egypt “Father of Geometry” Wrote the “Book of Elements” - set of 13 books with definitions, postulates, axioms, and theorems A postulate or axiom is an accepted fact. Postulate 1-1 Through any two points there is exactly one line A B l Postulate 1-2 If two lines intersect, then they intersect in exactly one point. C B A E D Postulate 1-3 If two planes intersect, then they intersect in exactly one line. Postulate 1-4 Through any three noncollinear points there is exactly one plane. S X B C Q Did You Get It?: