September 10, 2013 1) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.

1. September 10, 20131) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY. 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?

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

3. Review Triangle Theorems

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

5. Triangle Proofs – Example 2 • Given m∠EAB = 155° m∠ABC = 60° Prove m∠ ACD = 85° E B A C 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 • Green Team • Ben M. • Kathy M. • Christian V. • Brisya C. • Purple Team • Linda • Jovanny H. • Adolfo G. • Justlene S. • Red Team • George O. • Mayra R. • Charles L. • Ashley T. • Yellow Team • Oscar E. • Jazmin A. • Nancy L. • Miguel B. • Orange Team • Ben L. • Susana A. • Abel • Blue Team • Jose L. • Carina A. • Jackie D. • Diana O.

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

11. Geometry Period 6 Teams • Green Team • Christina R. • Geovanni B. • Oscar G. • Sabrina L. • Purple Team • Alexis A. • Deborah H. • Sabrina O. • Cristian B. • Red Team • Freddy A. • Anthony S. • Hannya O. • Ashley L. • Orange Team • Steven P. • Wendy G. • Leslie H. • Yellow Team • Paulina C. • Martin R. • Melissa R. • Jonathan T. • Blue Team • Jose S. • Jailene L. • Abigail G. • Andy 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 2 • . • . • . • Period 3 • . • . • . • . • Period 1 • . • . • . • . • Period 5 • Period 6 • Jose S. • Andy H. • Abigail. • . • Period 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 • Green Team • Kharla P. • Norma R. • George M. • Kate V. • Purple Team • Juda M. • Daniel P. • Lawrie S. • Jennifer B. • Red Team • Florian S. • Lupe V. • Ana G. • Julyssa M. • Yellow Team • Kenny C. • Jessica D. • Steven F. • Ashley S. • Orange Team • Rene M. • Susana F. • Lizette M. • Ashley V. • Blue Team • Alejandra P. • Evelyn C. • Mario L. • Monica G.

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

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

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

28. Geometry Period 6 Teams • Green Team • Christina R. • Geovanni B. • Oscar G. • Sabrina L. • Purple Team • Alexis A. • Deborah H. • Sabrina O. • Cristian B. • Red Team • Freddy A. • Anthony S. • Hannya O. • Ashley L. • Orange Team • Steven P. • Wendy G. • Leslie H. • Yellow Team • Paulina C. • Martin R. • Melissa R. • Jonathan T. • Blue Team • Jose S. • Jailene L. • Abigail G. • Andy 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 2 • Miguel B. • Jose L. • Jackie D. • Carina • Period 3 • Stephanie L. • Adrian D. • Armando H. • Karla L. • Period 1 • Mario L. • Evelyn C. • Alejandra P. • Monica G. • Period 5 • Period 6 • Oscar G. • Christina R. • Sabrina L. • Geo B. • Period 4 • Jesus R. • Ariana P. • Leslie V. • Eric M.

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, _____________________ .