Do Now

1. Do Now • I need a volunteer for the class job of pass-out specialist (benefit, you get a pass on Do Nows for the week) • Find the measure of angle b • Find the value of x.

2. Review • Name the angle types and solve for b in each angle.

3. Intro to Triangles Students will find measures of angles in triangles.

4. Video • http://www.youtube.com/watch?v=vw-rOqDBAvs&feature=related

5. Triangle Sum Theorem • Triangle Sum Theorem – the sum of the measures of the angles of a triangle is 180.

6. Example #1 • What is the measure of angle 1?

7. Example #1 • What is the measure of angle 1? • <1 = 180 – 37 – 57 = 86

8. How many Triangles?

9. How many Triangles? Answer: 3! ABD, BDC, and the big triangle ABC.

10. How many triangles?

11. Example #2 • Find the values of x, y, and z.

12. Example #2 • Find the values of x, y, and z. • 43 + 59 + x = 180. x = 180 – 59 – 43. x = 78 • x + y = 180. 78 + y = 180. y = 180 – 78. y = 102 • y + z + 49 = 180. 102 + z + 49 = 180. z = 180-49-102. z = 29.

13. Exterior Angle of a Polygon • Exterior Angle of a Polygon – an angle formed by a side and an extension of an adjacent side. • 1 • Remote Interior Angles – the two nonadjacent interior angles • 2 and 3

14. Name the exterior angle of the polygon and the remote interior anglesin the diagram below.

15. Triangle Exterior Angle Theorem • The measure of each exterior angle of a triangle equals the sum of its two remote interior angles.

16. Example #1 • What is the measure of angle 1?

17. Example #1 • What is the measure of angle 1? • <1 = 80 + 18 • <1 = 98

18. Example #2 • What is the measure of angle 2?

19. Example #2 • What is the measure of angle 2? • <2 + 59 = 124 • <2 = 124 – 59 • <2 = 65

20. You Try • On the back of your notes! • Find the values of the variables x, y, and z.

21. You Try • Find the values of the variables x, y, and z. • y = 36, z = 90, x = 38

22. You Try On the back of your notes: Find the values of the variables and the measures of the angles.

23. You Try On the back of your notes: Find the values of the variables and the measures of the angles. • (2x + 4) + (2x – 9) + x = 180 • x = 37

24. Exit Ticket Find the value of <1 in the diagram to the right Find the value of x, y, and z Solve for x. HOMEWORK!!!: Page 75 1,3,4,8,10,17,18

25. Do Now Find Find

26. Exit Ticket 10/1 Find the value of <1 in the diagram to the right Find the value of x, y, and z Solve for x. HOMEWORK!!!: Page 75 1,3,4,8,10,17,18

27. Congruent Figures Students will be able to find corresponding parts of congruent figures

28. Congruent Figures • Congruent figures have the same size and shape.

29. Congruent Figures • Congruent Polygonshave congruent corresponding parts - their sides and angles match!!

30. Congruent Figures • ***When naming congruent polygons, you MUST list the corresponding vertices in the SAME ORDER.

31. Video • http://app.discoveryeducation.com/player/view/assetGuid/A39E2AC4-E031-4E6A-8115-FC59EF04BF76

32. Let’s Practice! • WXYZ JKLM • Line segment WX  _?_ • Line segment KL  _?_ • Line segment MJ  _?_ • _?_ • _?_ • _?_

33. Let’s Practice • Complete the following statements: Given: ΔNMK ΔVYZ a) line segment line segment _?_ b) line segment line segment _?_ c) _?_ d) _?_

34. Let’s Practice!

35. Third Angles Theorem

36. You try! • What is

37. You try • , 72. What is ? (Draw a diagram to help you answer the question. Think back to the last problem)

38. Exit Ticket 10/2 • Complete the following statements: Given: ΔDEF ΔGZT a) line segment line segment _?_ b) _?_ • ∆ABC  ∆LMN. Name all of the pairs of corresponding congruent parts. (Draw a picture of the two triangles on a separate sheet of paper to help you answer the question.) • , . What is ? (Draw a diagram to help you answer the question.)

39. Do Now • Complete the following statements: Given: ΔSML ΔTNY a) line segment line segment _?_ b) _?_ • ∆QRS ∆TUV. Name all of the pairs of corresponding congruent parts. (Draw a picture of the two triangles on a separate sheet of paper to help you answer the question.) • , . What is ? (Draw a diagram to help you answer the question.)

40. Exit Ticket 10/2 • Complete the following statements: Given: ΔDEF ΔGZT a) line segment line segment _?_ b) _?_ • ∆ABC  ∆LMN. Name all of the pairs of corresponding congruent parts. (Draw a picture of the two triangles on a separate sheet of paper to help you answer the question.) • , . What is ? (Draw a diagram to help you answer the question.)

41. Yesterday we learned that… • … two polygons were congruent if all sides AND all angles were congruent. • But that’s WAY more info than we need!!

42. Today we will learn… • …how to prove that two triangles are congruent by using: • 3 pairs of corresponding sides • 2 pairs of corresponding sides and 1 pair of corresponding angles • 1 pair of corresponding sides and 2 pairs of corresponding angles

43. Tick Marks and Curves What do those red tick marks and curves mean?

44. You Try! • The single tick mark means line segment NJ _?_ • The double tick marks mean FR _?_ • The curve means_?_

45. Side-Side-Side Postulate (SSS)

46. Side-Angle-Side Postulate (SAS)

47. Identifying Congruent Triangles Look at the triangles: • How many congruent sides do we have (count the sets of tick marks). • How many congruent angles do we have ? • Are the angles between the sides? • Are the triangles congruent? Justify.

48. Identifying Congruent Triangles Look at the triangles: • How many congruent sides do we have (count the sets of tick marks). • How many congruent angles do we have ? • Are the angles between the sides? • Are the triangles congruent? Justify.

49. Identifying Congruent Triangles Would you use SSS or SAS to prove the triangles congruent? If there is not enough information, write not enough information.

50. Identifying Triangles with Funky Shapes Are the following triangles congruent? Justify.