1. 6/24/2010 ©Evergreen Public Schools 2010 1 Triangle Sum Theorem Vocabulary : flowchart theorem

2. ©Evergreen Public Schools 2010 2 Learning Target I can prove the Triangle Sum Theorem. Name any theorems you know.

3. ©Evergreen Public Schools 2010 3 LaunchLaunch You turn on a lamp, and it doesn’t work. What would you do to get it to work?

4. ©Evergreen Public Schools 2010 4 LaunchLaunch This flow chart shows a process you could use.

5. ©Evergreen Public Schools 2010 5 LaunchLaunch Make your own flowchart that can be used to make a peanut butter and jelly sandwich.

6. ©Evergreen Public Schools 2010 6 ExploreExplore

7. 7 Before we play any game, like Monopoly, we need to agree on rules. Pass Go, Collect $200

8. ©Evergreen Public Schools 2010 8 What is acceptable in a game or society depends on the agreements. Collect money from some who lands on your property.

9. ©Evergreen Public Schools 2010 9 To be a citizen in a country agree to the Constitution and Bill of Rights. First Amendment: Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

10. ©Evergreen Public Schools 2010 10 As a consequence of the First Amendment In Tinker v. Des Moines Independent Community School District, 393 U.S. 503 (1969), the Supreme Court extended free speech rights to students in school. The case involved several students who were punished for wearing black armbands to protest the Vietnam War. The Supreme Court ruled that the school could not restrict symbolic speech that did not cause undue interruptions of school activities. Tinker v. Des Moines Independent Community School DistrictU.S.503 Vietnam War

11. ©Evergreen Public Schools 2010 11 Before we begin, we need to make agreements. There are terms what we can draw and describe, but do not define. point line plane

12. ©Evergreen Public Schools 2010 12 Definitions are true. Define triangle parallel lines

13. ©Evergreen Public Schools 2010 13 In this class, the world is flat. What do you think? Still don’t believe me? Describe the top of the white board. Describe the shape of the parking lot. How many degrees are in a triangle?

14. ©Evergreen Public Schools 2010 14 How many degrees are in a triangle? What does a triangle look like on a globe or an orange?

15. ©Evergreen Public Schools 2010 15 Use a straightedge to draw a line on your paper. 1)How many lines can you draw that are parallel to that line? Draw a point on your paper. 2) How many lines can you draw that are parallel to your original line and pass through your point?

16. ©Evergreen Public Schools 2010 16 There is exactly one line that is parallel to a given line through a given point. Statements that we agree to be true are called postulates.

17. ©Evergreen Public Schools 2010 17 Triangle Sum Theorem Why do you believe ?

18. ©Evergreen Public Schools 2010 18 Why do you believe ?

19. ©Evergreen Public Schools 2010 19 Why do you believe ?

20. ©Evergreen Public Schools 2010 20 What kind of reasoning did we use? Did anyone find a counterexample? We use deductive reasoning to prove it is always true. So we believe

21. ©Evergreen Public Schools 2010 21 We want to prove ABC is a triangle This is given to us. Draw auxiliary line BD so that AC || BD. There is exactly one line that is parallel to a given line through a given point. DD

22. ©Evergreen Public Schools 2010 22 We want to prove AC || BD. … exactly one … parallel … line … If parallel lines are cut by a transversal, then alternate interior angles are congruent. Together the three angles form a straight angle which is 180°.

23. ©Evergreen Public Schools 2010 23 We want to prove AC || BD substitution This is what we wanted to prove.

24. ©Evergreen Public Schools 2010 24

25. A Path to Theorems ABCSum 895041180 1273023180 906030180 ©Evergreen Public Schools 2010 25 We use inductive reasoning to make a conjecture.

26. A Path to Theorems ©Evergreen Public Schools 2010 26 Can we find a counterexample? Let’s see a bunch of triangles online.online Since we can’t find a counterexample we think this is true. We use deductive reasoning to prove it is always true.

27. A Path to Theorems ©Evergreen Public Schools 2010 27 We use deductive reasoning to prove it is always true. We write a logical sequence of steps. Each step is justified. –What do we use for the justifications?

28. ©Evergreen Public Schools 2010 28 Debrief How do we get from a conjecture to a theorem? How do we develop the sequence of steps in the flowchart? Where do the justifications come from?

29. ©Evergreen Public Schools 2010 29 5 3 1 2 4 Learning Target Did you hit the target? I can prove the Triangle Sum Theorem. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

30. ©Evergreen Public Schools 2010 30 Put the arrows into the flowchart proof. Given Given Supplementary angles substitution add to 180 Supplementary angles add to 180