1. Chapter 1 Introduction to Geometry

2. Slide 2 1.1 Getting Started Points – To name a point always use Lines – All lines are and extend in both directions. To name a line use on the line. Line Segment – Has a definite and, called. To name a segment use. Ray – Begins at and then extends in one direction. To name a ray you must name the first and then on the ray.

3. Slide 3 1.1 Getting Started Angle – Two with the same form an angle. The common is called the, and the two are called the. Triangle –To name a triangle use of the triangle. Union ( ) – What do the objects ? Intersection (∩) – What do the objects ?

4. Slide 4 1.1 Example

5. Slide 5 1.2 Measurement of Segments and Angles Measuring Segments Find AB. Classifying Angles Acute: Angle measures Right: Angle measures Obtuse: Angle measures Straight: Angle measures

6. Slide 6 1.2 Measurement of Segments and Angles Measuring Angles 60 minutes = 60 seconds = Congruent ( ) Two angles with the Two segments with the On diagrams we use to indicate congruent parts.

7. Slide 7 1.2 Examples

8. Slide 8 1.2 Examples

9. Slide 9 1.3 Collinearity, Betweenness, and Assumptions Collinear – Points that lie on Noncollinear – Points that Betweenness of Points – All three points must be Triangle Inequality – The sum of the lengths of any is always than the length of the You should assume from a diagram… 1) Straight lines and angles 2) Collinearity of points 3) Betweenness of points 4) Relative positions of points

10. Slide 10 1.3 Examples

11. Slide 11 1.3 Examples

12. Slide 12 1.4 Beginning Proofs StatementsReasons Theorem – A mathematical model that can be.

13. Slide 13 1.4 Examples StatementsReasons

14. Slide 14 1.4 Examples StatementsReasons

15. Slide 15 1.5 Division of Segments and Angles Bisect – Divide a segment or angle into parts On a segment the bisection point is called the. In an angle, the dividing ray is called the. Trisect – Divide a segment or angle into parts On a segment, the two points that divide the segment are called. In an angle, the two dividing rays are called.

16. Slide 16 1.5 Examples StatementsReasons

17. Slide 17 1.5 Examples StatementsReasons

18. Slide 18 1.5 Examples StatementsReasons

19. Slide 19 1.7 Deductive Structure & 1.8 Statements of Logic Conditional Statement: If p, then q. Hypothesis: Conclusion: Negation: Every conditional statement has three other statements. 1.Converse – hypothesis and conclusion 2.Inverse – hypothesis and conclusion 3.Contrapositive – hypothesis and conclusion Theorem 3: If a conditional statement is true, then the of the statement is also true.

20. Slide 20 1.7 & 1.8 Examples If Joe is a member of the RB soccer team, then he is a student at RB. 1)Write the converse. 2) Write the inverse. 3) Write the contrapositive. 4) Are the above statements true?

21. Slide 21 1.7 & 1.8 Examples What conclusion can you draw given:

22. Slide 22 1.9 Probability

23. Slide 23 1.9 Example