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 Noncollinear – A, B, D or C, B, E or A, B, C or D, B, E Must have commas! Otherwise you are naming a plane.

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