1. Learning Goal:  IWBAT to solve for unknown angles in triangles by writing geometric proofs. Homework :  HW 3.3B: Exterior Angle Theorem Worksheet ------------------------------------------------------------------- Do Now:  Suppose you had four straws with the given side lengths: 5cm, 7cm, 19cm, 13 cm  Which three straws will form a triangle? Why? September 10, 2013 1) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.

2. Agenda: 1.Do Now (15 min) 2.Triangle Proofs Lecture (30 min) 3.Triangle Proofs Card Sorts (35 min) 4.Triangle Algebra Activity (35 min) 5.Closure (5 min)

3. Review Triangle Theorems

4. Triangle Proofs – Example 1  Given m ∠ ABC = 30° m ∠ BCA = 20° Prove m ∠ DAE = 130° B C A E D

5. Triangle Proofs – Example 2  Given m ∠ EAB = 155° m ∠ ABC = 60° Prove m ∠ ACD = 85° B C A E D

6. Triangle Proofs – Example 3  Given m ∠ RPQ = 30° m ∠ PQR = (4x+2)° m ∠ HRQ = (8+6x)°  Prove x = 12

7. Triangle Proofs Activity  You will work with the person sitting next to you. Each pair will receive paper cut-outs containing the steps of a geometric proof to a triangle problem.  Each geometric proof is color coded to make it easier for you to arrange the paper cut-outs.  Your task is to arrange the paper cut-outs into a two-column proof. Then copy the proof in your notes.  The teacher will ask certain pairs to present their geometric proof to the class.

8. Triangle Algebra Activity  Students break up into groups of 3 or 4. Groups have been predetermined. Each group receives a whiteboard, marker, and eraser.  Teacher will present practice exercises about triangles on the board.  Your teams have 2 minutes to solve the problem and write the answer on the whiteboard with its justification.  The correct answer receives 1 point. The correct justification receives an additional point.

9. Geometry Period 2 Teams  Red Team 1.George O. 2.Mayra R. 3.Charles L. 4.Ashley T.  Green Team 1.Ben M. 2.Kathy M. 3.Christian V. 4.Brisya C.  Blue Team 1.Jose L. 2.Carina A. 3.Jackie D. 4.Diana O.  Yellow Team 1.Oscar E. 2.Jazmin A. 3.Nancy L. 4.Miguel B.  Purple Team 1.Linda 2.Jovanny H. 3.Adolfo G. 4.Justlene S.  Orange Team 1.Ben L. 2.Susana A. 3.Abel

10. Geometry Period 4 Teams  Red Team 1.Dennise P. 2.Amanda V. 3.Seth F. 4.Javier G.  Green Team 1.Veronica S. 2.Arthur D. 3.Lorena G. 4.Alfonso M.  Blue Team 1.Angie Z. 2.Miranda D. 3.Sydney G. 4.Oscar S.  Yellow Team 1.Jesus R. 2.Ariana P. 3.Leslie V. 4.Erick M.  Purple Team 1.James L. 2.Lee Ann Q. 3.Mirna A. 4.Thea Q.  Orange Team 1.Christina G. 2.Derek A. 3.Yuleni V.

11. Geometry Period 6 Teams  Red Team 1.Freddy A. 2.Anthony S. 3.Hannya O. 4.Ashley L.  Green Team 1.Christina R. 2.Geovanni B. 3.Oscar G. 4.Sabrina L.  Blue Team 1.Jose S. 2.Jailene L. 3.Abigail G. 4.Andy H.  Yellow Team 1.Paulina C. 2.Martin R. 3.Melissa R. 4.Jonathan T.  Purple Team 1.Alexis A. 2.Deborah H. 3.Sabrina O. 4.Cristian B.  Orange Team 1.Steven P. 2.Wendy G. 3.Leslie H.

12. Exercise #1  Find the measure of the unknown angle shown below.

13. Exercise #2  Find the measure of the unknown angle shown below.

14. Exercise #3  Find the measure of the unknown angle shown below.

15. Exercise #4  Find the measure of the unknown angle shown below.

16. Exercise #5  Find the value of x shown below.

17. Exercise #6  Find the value of x shown below.

18. Exercise #7  Find the value of x shown below.

19. Exercise #8  Find the value of x shown below.

20. Exercise #9

21. Exercise #10

22. Exterior Angle Theorem Masters  Period 1 1.. 2.. 3.. 4..  Period 2 1.. 2.. 3..  Period 4 1.. 2.. 3.. 4..  Period 5  Period 3 1.. 2.. 3.. 4..  Period 6 1.Jose S. 2.Andy H. 3.Abigail. 4..

23. Triangle Algebra Activity  Students break up into groups of 3 or 4. Groups have been predetermined. Each group receives a whiteboard, marker, and eraser.  Teacher will present practice exercises about triangles on the board.  Your teams have 2 minutes to solve the problem and write the answer on the whiteboard with its justification.  The correct answer receives 1 point. The correct justification receives an additional point.

24. Geometry Period 1 Teams  Red Team 1.Florian S. 2.Lupe V. 3.Ana G. 4.Julyssa M.  Green Team 1.Kharla P. 2.Norma R. 3.George M. 4.Kate V.  Blue Team 1.Alejandra P. 2.Evelyn C. 3.Mario L. 4.Monica G.  Yellow Team 1.Kenny C. 2.Jessica D. 3.Steven F. 4.Ashley S.  Purple Team 1.Juda M. 2.Daniel P. 3.Lawrie S. 4.Jennifer B.  Orange Team 1.Rene M. 2.Susana F. 3.Lizette M. 4.Ashley V.

25. Geometry Period 2 Teams  Red Team 1.George O. 2.Mayra R. 3.Charles L. 4.Ashley T.  Green Team 1.Ben M. 2.Kathy M. 3.Christian V. 4.Brisya C.  Blue Team 1.Jose L. 2.Carina A. 3.Jackie D. 4.Miguel B.  Yellow Team 1.Oscar E. 2.Jazmin A. 3.Nancy L.  Purple Team 1.Linda 2.Jovanny H. 3.Adolfo G. 4.Justlene S.  Orange Team 1.Ben L. 2.Susana A. 3.Abel P.

26. Geometry Period 3 Teams  Red Team 1.Alexis A. 2.Nathone G. 3.Kimberly M. 4.June M.  Green Team 1.Silver H. 2.Christian D. 3.Raquel P. 4.Julio Q.  Blue Team 1.Stephanie S. 2.Alanis G. 3.Daniel T. 4.Alice S.  Yellow Team 1.Anika G. 2.Sarah J. 3.Matthew D. 4.Andrea Q.  Purple Team 1.Stephanie L. 2.Adrian D. 3.Armando H. 4.Karla L.  Orange Team 1.Erica C. 2.Jose S. 3.Jorge A. 4.Kate R.

27. Geometry Period 4 Teams  Red Team 1.Dennise P. 2.Amanda V. 3.Seth F. 4.Javier G.  Green Team 1.Veronica S. 2.Arthur D. 3.Lorena G. 4.Alfonso M.  Blue Team 1.Angie Z. 2.Miranda D. 3.Sydney G. 4.Oscar S.  Yellow Team 1.Jesus R. 2.Ariana P. 3.Leslie V. 4.Erick M.  Purple Team 1.James L. 2.Lee Ann Q. 3.Mirna A. 4.Thea Q.  Orange Team 1.Christina G. 2.Derek A. 3.Yuleni V.

28. Geometry Period 6 Teams  Red Team 1.Freddy A. 2.Anthony S. 3.Hannya O. 4.Ashley L.  Green Team 1.Christina R. 2.Geovanni B. 3.Oscar G. 4.Sabrina L.  Blue Team 1.Jose S. 2.Jailene L. 3.Abigail G. 4.Andy H.  Yellow Team 1.Paulina C. 2.Martin R. 3.Melissa R. 4.Jonathan T.  Purple Team 1.Alexis A. 2.Deborah H. 3.Sabrina O. 4.Cristian B.  Orange Team 1.Steven P. 2.Wendy G. 3.Leslie H.

29. Exercise #1  Find the measure of the unknown angle shown below.

30. Exercise #2  Find the measure of the unknown angle shown below.

31. Exercise #3  Find the measure of the unknown angle shown below.

32. Exercise #4  Find the measure of the unknown angle shown below.

33. Exercise #5  Find the measure of the unknown angle shown below.

34. Exercise #6  Find the measure of the unknown angle shown below.

35. Exercise #7  Find the measure of the unknown angle shown below.

36. Exercise #8  Find the measure of the unknown angle shown below.

37. Exercise #9  Find the measure of the unknown angle shown below.

38. Exercise #10  Find the measure of the unknown angle shown below.

39. Triangle Sum Theorem Masters  Period 1 1.Mario L. 2.Evelyn C. 3.Alejandra P. 4.Monica G.  Period 2 1.Miguel B. 2.Jose L. 3.Jackie D. 4.Carina  Period 4 1.Jesus R. 2.Ariana P. 3.Leslie V. 4.Eric M.  Period 5  Period 3 1.Stephanie L. 2.Adrian D. 3.Armando H. 4.Karla L.  Period 6 1.Oscar G. 2.Christina R. 3.Sabrina L. 4.Geo B.

40. Closure Take a moment to response to the following prompts on a flashcard.  Why do the angles of any triangle add up to 180 degrees?  The angles of any triangle add up to 180 degrees because ___________________________.  What conditions must three sides satisfy in order for the sides to form a triangle?  In order for sides to form a triangle, _____________________.