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Applied Geometry

Applied Geometry. Lesson 1-2 Points, Lines, and Planes. Objective: Learn to identify and draw models of points, lines, and planes, and determine their characteristics. Point – the basic unit of geometry. Has no size. Named using CAPITAL Letters. Read as point A.

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Applied Geometry

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  1. Applied Geometry Lesson 1-2 Points, Lines, and Planes Objective: Learn to identify and draw models of points, lines, and planes, and determine their characteristics.

  2. Point –the basic unit of geometry Has no size Named using CAPITAL Letters Read as point A

  3. Line– a series of points that extends without end in two directions. Made up of an infinite number of points Arrows show that the line extends without end in both directions Named: either a single lowercase script letter OR 2 points on the line Named: line l or

  4. Example 1 • Name two points on line m • Give 3 names for the line point P and point Q (or Point R)

  5. Definitions • Collinear– points that lie on the same line • Noncollinear– points that do not lie on the same line.

  6. Example 3 • Name three points that are collinear and three points that are noncollinear. Collinear – A, B, E or D, B, C Must have commas! Otherwise you are naming a plane. Noncollinear – A, B, D or C, B, E or A, B, C or D, B, E

  7. Ray– has a definite starting point and extends without end in one direction. The starting point of a ray is called the endpoint. A ray is named using the endpoint first, then another point on the ray. *Naming a ray: arrow always points right!

  8. Ray cont… • Look at the pairs of rays

  9. Line Segment –a part of a line consisting of 2 endpoints and all points between • Name using its endpoints

  10. Example • Name 2 segments and one ray. Don’t name the same thing twice unless it asked for the different ways of naming. Sample answers: Why does ray BD not work?

  11. Plane –a flat surface that extends without end in all directions • For any 3 noncollinear points, there is only one plane that contains all 3 points. • A plane can be named with a single uppercase script letter or by three noncollinear points. Plane named: ABC or M

  12. Definitions • Coplanar – Points that lie in the same plane • Noncoplanar – Points that do not lie in the same plane.

  13. Hands-On Activity • Place points B, C, D, E near the corners of a piece of paper. • Place point A in the middle of the paper • Fold the paper so that point A is on the crease. • Open the paper slightly. The two sections of the paper represent different planes. • Name 3 points that are coplanar • Name 3 points that are noncoplanar • Name a point that is in both planes A, E, D D, A, C A

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