1. Geometry 1.1 Basic Geometric Objects

2. 1.1 Basic Geometric Objects The 3 Undefined Terms of Geometry represent these three objects… Points Lines (and portions of lines: segments and rays) Plane (will be studied later in text) Every object in geometry has a Definition (except the above trio) Symbol or Name Image or Diagram 1.1 Basic Geometric Objects

3. Points Points are location without substance. They have neither size nor dimension. Points are imperfectly represented in a diagram by a small dot (this dot is not so small). A capital letter is used to name a point as we see above. A 1.1 Basic Geometric Objects

4. In Algebra, points are represented by ordered pairs of numbers (x, y). Points make up every algebraic curve. For example, the collection of points that satisfy the following equations create the curves shown below each. 1.1 Basic Geometric Objects

5. 5 Lines When we talk about lines in geometry we are talking about straight lines that extend forever in both directions. They never end. Below is a picture of a line. When we draw a line we put arrows on the ends to signify that the line keeps going.

6. 6 Lines (Continued) There are two ways to name a line. One way is to use a lowercase letter (usually l, m, n, p, q, r, s, or t) as in the figure below. m

7. 7 How many points are on a line? – Infinitely Many! More importantly…how many points determine a line? – Exactly two. (Therefore) another way to name a line is by using two points on the line. A B Name of LineDiagram of Line or

8. 8 Lines (Continued) So, to name a line by using two points, we write the two capital letters of the points next to each other and then draw a little line symbol over them. It doesn’t matter which letter comes first. Important: the line symbol above the letters has arrows on both ends.

9. The Number Line (a ruler) 1.1 Basic Geometric Objects To every point on line there corresponds a unique real number. To every real number there corresponds a unique point on the line.

10. 10 Line Segments Line segments are straight and they have two endpoints. Line segments come in various lengths. Line segments are parts of lines. Below is a picture of a line segment. When we draw one, we usually use dots to emphasize the endpoints.

11. 11 There is only one way we will name line segments. We name them by using their endpoints. A B PictureName or

12. 12 When naming a line segment we draw a picture of a line segment (without arrows or dots on the ends) above the two capital letters denoting the endpoints. Note well the difference between the name of a line and the name of a line segment: LineLine Segment

13. 13 Rays A ray is straight and it has one endpoint. A ray extends forever in one direction. Imagine a line (not a line segment). If you break the line into two pieces, each piece will be a ray. Below is a picture of a ray. We draw an arrow on one end and a dot on the other end. endpoint

14. 14 Rays (continued) We name a ray by using its endpoint and any other point on the ray. We always write the endpoint first, then the other point, and then we draw a picture of a ray above the letters. CD PictureName

15. 15 Summary line m A B m A B A B line line segment ray

16. The Defined Terms of Geometry are all defined in terms of the undefined terms or previously defined terms Points, Lines, Line Segments and Rays Points, Lines, Line Segments and Rays – These are the undefined terms – These are the building blocks of all other geometric objects 1.1 Basic Geometric Objects

17. Vocabulary Word: Angle Diagram: Definition: an angle is the union of two _____ with a common ________. A B C rays endpoint

18. A B C Symbol:  Name it by: Its Vertex  A A number  1 3 Points  BAC Point A is called the vertex Point A is called the vertex Vertex letter must be in the middle Vertex letter must be in the middle The rays are called the sides The rays are called the sides 1

19. Vocabulary Word: Triangle Diagram: Definition: a triangle is the union of three ______________. A B C line segments