Happy Wednesday!

1. Happy Wednesday! • Pick up notes and take out homework Tonight’s HW: • P 227 #12-14 • P 234 #1-11 • P 245 # 1-7 • Make notecards from U2L7 and U2L8 (definition one side and vocab. word on the other side • Updates: • Unit 2 Quiz 2 (4.1-4.4) Monday 10/27

2. Agenda • Review HW/ Warm- Up! • Notecard War! • Finish 4.2 • 4.3: Congruent Triangles • 4.4: Triangle Congruence: SSS and SAS • Cool-Down…

3. Stamping I am going to stamp your homework and the worksheet on the back of your 4.1 notes. HAVE IT OUT AND READY! If it is not out on your desk when I come by, you will NOT get a STAMP! While I am doing this , you are going to be doing whiteboards. If I come around and you are NOT working on whiteboards, you will be docked participation points.

4. Stamping I am going to stamp your homework and the worksheet on the back of your 4.1 notes. HAVE IT OUT AND READY! If it is not out on your desk when I come by, you will NOT get a STAMP! While I am doing this , you are going to be doing whiteboards. If I come around and you are NOT working on whiteboards, you will be docked participation points.

5. Whiteboards Find mACD.

6. Whiteboards Afteran accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find the following: mXYZ. mYWZ

7. Review HW (p 219 #1-11) 2. One of the angles is obtuse and the other two angles are acute 4.Right 6. Isosceles 8. Scalene 10. 3.1. 3.1, 3.3

8. Review HW (p 227 # 4-11, 24) 4. 17 6. 69.2 8. 65 1/3 10. 41 • a. Given, b. m <F= 90 c. Triangle Sum Theoremd. Substitutione. m<D +m<E= 90 f. Def of complementary angles

9. Review HW (Worksheet on back of 4.1) On Doc Cam

10. How do we Use Notecards Effectively? Any ideas? You are going to pair up with someone at your table. Person 1 will go first and show your partner your vocab word. Person 2 will say everything they know about the vocab word. You will go through your deck until you are done. Then SWITCH! Keep doing this until you get the entire pile of notecards CORRECT!

11. How do we Use Notecards Effectively? We will do this every block period since this Unit is a lot of vocab 

12. 4.2 Continued… We did not finish 4.2 note so please take them out 

13. Third Angle Theorem

14. Example 4: Applying the Third Angle Theorem Find mK and mJ.

15. Whiteboards Find mPand mT.

16. Learning Objective(s) By the end of this period you will be able to: • Use properties of congruent triangles • Apply SSS and SAS to construct triangles and to solve problems

17. Congruent Triangles Corresponding angles and corresponding sides • Same position in polygons with an equal number of sides Congruent Polygons • If corresponding sides are congruent

18. Congruent Triangles Congruent Triangles • triangles that are the same shapeand size. • Two triangles are congruent if and only if their corresponding parts are congruent. • Corresponding angles and corresponding sides are in the sameposition in the triangle • Name congruent triangles using Congruence Statements. Congruence Statements orders the vertices based on the congruentparts. • ORDER MATTERS!

19. Congruent Triangles Congruence Statement: Corresponding Congruent Angles: Corresponding Congruent Sides:

20. EX 1: Naming Congruent Corresponding Parts Given: ∆PQR ∆STW Identify all pairs of corresponding congruent parts. Angles: P  S, Q  T, R  W Sides: PQ ST, QR  TW, PR  SW

21. Example 1 (b)

22. Example 2: Using Corresponding Parts of Congruent Triangles Given: ∆ABC ∆DBC. • Find the value of x. • Find mDBC.

23. Whiteboards Given: ∆ABC  ∆DEF • Find the value of x.. 2. Find mF.

24. Example 3

25. Whiteboards Do the following problem on your whiteboard individually. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB.

26. Whiteboard Activity Find another student in the room. You must choose a student who has: (1) A name starting with the same letter as yours OR (2) A last name starting with the same letter as yours. These people CANNOT be at your table! You will be checking your partners work. If the students see a mistake in your work they are to help correct your mistake.

27. Whiteboards Do the following problem on your whiteboard individually. • Given that polygon MNOP polygon QRST, identify the congruent corresponding part. • a. NO  ____ b. T  ____

28. Whiteboard Activity Find another student in the room ( who you did not choose for #1). You must choose a student who has: (1) A name starting with the same letter as yours OR (2) A last name starting with the same letter as yours. These people CANNOT be at your table! You will be checking your partners work. If the students see a mistake in your work they are to help correct your mistake.

29. Math Joke of the Day • What do you call a fierce beast? • A line

30. 4.4: Triangle Congruence: SSS and SAS Learning Objective • SWBAT apply SSS and SAS to show triangles are congruent. • SWBAT prove triangles are congruent by using SSS and SAS.

31. SSS and SAS Congruence (4.4) Instead of having to prove that all sides and angles are congruent in order to prove that triangles are congruent, we are going to learn 5 shortcuts. There are five ways to prove triangles are congruent: • SSS • SAS • ASA • AAS • HL Today we are going to discuss SSS and SAS.

32. 4-4 Triangle Congruence: SSS and SAS Side–Side–Side Congruence (SSS) • If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. • We abbreviate Side-Side-Side Congruence as SSS. What is a possible congruent statement for the figures?

33. Examples • Non-Examples

34. 4-4 Triangle Congruence: SSS and SAS • Included Angle • An angle formed by two adjacent sides of a polygon. • B is the included angle between sides ABand BC.

35. Whiteboards • What is the included angle between the sides BC and CA? • What are the sides of the included angle A?

36. Side-Angle-Side Congruence Side–Angle–Side Congruence (SAS) • If two sides and the included angleof one triangle are congruent to two sidesand the included angle of another triangle, then the triangles are congruent. What is the possible congruence statement for the figures?

37. Example/ Non-Examples • Example • Non-Example

38. 4-4 Triangle Congruence: SSS and SAS Example 1: • Use SSS to explain why ∆ABC  ∆DBC. Use the following sentence frame: It is given that ____  ____ and __  ______ By the ___________________________, ____ _____. Therefore ________  _________ by ________

39. Whiteboards Explain why ∆ABC  ∆CDA. It is given that ____  ____ and __  ______ By the ___________ ____________ of Congruence, ____ _____. Therefore ________  _________ by ________

40. 4-4 Triangle Congruence: SSS and SAS Example 1(b) : Explain why ∆XYZ  ∆VWZ. It is given that ____  ____ and __  ______ By the __________________________________________, ____ _____. Therefore ________  _________ by ________

41. Whiteboards Explain why ∆ABC  ∆DBC. I am not going to to give you thesentence frame, but I still want you to use complete sentences. Follow what you have on your notes. It is given that BA BD and ABC  DBC. By the Reflexive Property of , BC  BC. So ∆ABC  ∆DBC by SAS.

42. Example 2: Verifying Triangle Congruence Show that the triangles are congruent for the given value of the variable. ∆MNO  ∆PQR, when x = 5. PQ  MN, QR  NO, PR  MO ∆MNO  ∆PQR by SSS.

43. ST  VW, TU  WX, and T  W. Whiteboards Show that the triangles are congruent for the given value of the variable. ∆STU  ∆VWX, when y = 4. ∆STU  ∆VWX by SAS.

44. 4-4 Triangle Congruence: SSS and SAS Example 3: The Hatfield and McCoy families are feuding over some land. Neither family will be satisfied unless the two triangular fields are exactly the same size. You know that BC is parallel to AD and the midpoint of each of the intersecting segments. Write a two-column proof that will settle the dispute. . Prove: ∆ABC ∆CDB Proof: Given: BC|| AD, BC AD

45. Closure Questions Which postulate, if any, can be used to prove the triangles congruent? In one sentence tell why or why not the triangles are congruent. 1. 2.

46. Begin Homework For the remaining time please begin the homework. If you get stuck: • Talk to your tablemates. • If all of your tablemates are confused raise your hand and I will assist you as soon as I can.