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1.2 Points, Lines, and Planes 9/10/12

1.2 Points, Lines, and Planes 9/10/12. Geometry – a mathematical system built on accepted facts, basic terms, and definitions. Undefined Terms – the basic ideas that you can use to build the definitions of all other figures in geometry.

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1.2 Points, Lines, and Planes 9/10/12

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  1. 1.2 Points, Lines, and Planes 9/10/12 • Geometry – a mathematical system built on accepted facts, basic terms, and definitions. • Undefined Terms – the basic ideas that you can use to build the definitions of all other figures in geometry. • You cannot define undefined terms, but it is important to have a general description of their meanings.

  2. Undefined Terms • Point – indicates a location and has no size. • Represent a point by a dot. • Name it with a capital letter, such as A. • Line – represented by a straight path that extends in two opposite directions without end and has no thickness. • A line contains infinitely many points. • Can name a line by any two points on the line, or by a single lowercase letter. • Plane – represented by a flat surface that extends without end and has no thickness. • Contains infinitely many lines. • Can name a plane by a capital letter or by at least three points in the plane that do not all lie on the same line.

  3. Undefined Terms Point A line l or AB plane P or plane ABC

  4. Points • Collinear points – points that lie on the same line. • Coplanar points – points that lie in the same plane. • All the points of a line are coplanar.

  5. Naming Points, Lines, and Planes • What are two other ways to name QT? • 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?

  6. Naming Points, Lines, and Planes • TQ and line m. • Plane RQV and plane RSV. • Points R, Q, and S are collinear. • Points R, Q, S, and V are coplanar.

  7. Defined Terms • Segment – a part of a line that consists of two endpoints and all points between them. • Can name a segment by its two endpoints. • Ray – a part of a line that consists of one endpoint and all the points of the line on one side of the endpoint. • Can name a ray by its endpoint and another point on the ray. • The order of points indicates the ray’s direction. • Opposite rays – two rays that share the same endpoint and form a line. • Can name opposite rays by their shared endpoint and any other point on each ray.

  8. Defined Terms AB AB CA and CB

  9. Name Segments and Rays • What are the names of the segments in the figure? • What are the names of the rays in the figure? • Which of the rays in the previous question are opposite rays?

  10. Name Segments and Rays • The three segments are DE or ED, EF or FE, and DF or FD. • The four rays are DE or DF, ED, EF, and FD or FE. • The opposite rays are ED and EF.

  11. Postulates • A postulate or axiom is an accepted statement of fact. • Basic building blocks of the logical system in geometry. • Use logical reasoning to prove general concepts.

  12. Postulates • Postulate 1.1 • Through any two points there is exactly one line. • When you have two or more geometric 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.

  13. Postulates • Postulate 1.3 • If two distinct planes intersect, then they intersect in exactly one LINE. • Postulate 1.4 • Through any three NONCOLLINEAR points, there is exactly one plane.

  14. More Practice!!!!! • Classwork – Textbook p. 16 - 17 # 9 – 35 odd • Homework – Textbook p. 16 - 17 # 8 – 36 even

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