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Points, Lines, and Planes

Points, Lines, and Planes

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Points, Lines, and Planes

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  1. Points, Lines, and Planes Geometry Mrs. King Unit 1, Lesson 2

  2. A P Q Z Definition Point: a location in space. A point has no size, but is represented by a dot labeled with a capital letter.

  3. Definition Space: the set of all points

  4. l Q P Definition Line: a series of points that extends without end in two opposite directions.

  5. Q R P Definition Collinear: points that lie on the same line.

  6. In the figure below, name three points that are collinear and three points that are not collinear. Practice Points Y, Z, and W lie on a line, so they are collinear. For example, X, Y, and Z and X, W, and Z form triangles and are not collinear.

  7. Definition Plane: a flat surface that extends in all directions without end.

  8. Shade the plane that contains X, Y, and Z. Practice

  9. Practice Name the plane shown in two different ways. You can name a plane using any three or more points on that plane that are not collinear. Some possible names for the plane shown are: plane RST plane RSU plane RTU plane STU plane RSTU

  10. Definition Coplanar: points and lines that are in the same plane.

  11. Practice • How many planes are represented by the surfaces of the cube? • Name the plane of the front of the cube in two different ways. • Name a point that is coplanar with the given points: • E, F, G • B, C, G

  12. Definition Postulate: an accepted statement of fact.

  13. Four Basic Postulates 1-1: Through any two points there is exactly one line. 1-2: If two lines intersect, then they intersect in exactly one point. 1-3: If two planes intersect, then they intersect in a line. 1-4: Through any three noncollinear points there is exactly one plane.

  14. Homework Points, Lines, and Planes in Student Practice Packet (Page 3, #1-21)