Triangle Theorems and Congruent Triangles

1. Unit 4 TRIANGLE FUN 

2. I can use the angle sum theorem • I can use the angle sum theorem • I can the exterior angle theorem • I can the exterior angle theorem Learning Targets Lesson 4-1

3. sum angles 180°

4. 30° m∠1 = 28° m∠1 = 120°

5. 58° 32° 32° 58° m∠1 = 56° m∠2 = 56° m∠3 = 74°

6. remote interior exterior not

7. exterior angle sum remote interior angles m∠1 = m∠A + m∠B

8. m∠1 = 115°

9. 2x + 95 = 145 2x = 50 x = 25

10. 140° 65° 40° 75° 115°

11. 55° 55° 70°

12. 125° 55° 95°

13. ASSIGNMENT: 4-1Worksheet

14. 4.2 Congruent Triangles Learning Target: • I can name and label corresponding parts of congruent triangles.

15. vertices A B C

16. size shape

17. Angle Measure Betweenness Collinearity Distance

18. m∠A = m∠J JK AB = m∠B = m∠K BC = KL m∠L JL m∠C = AC = Match up the letters in the same “position” AND look at the ‘tick marks’ in the picture! Match the congruent pieces!

21. Warm Up

24. I can recognize and use the SSS, SAS, ASA, AAS, and HL Postulates to see if triangles are the same. Lesson 4.3

26. CAN’T USE!!! 40 40 50 50

27. CAN’T USE!!! 7 7 6 6 40° 40°

29. SAS ∆DNV ≅ ∆BCX

30. SSS ∆TRS ≅ ∆SUT

31. HL ∆JKL ≅ ∆MNP

32. AAS ∆NJK ≅ ∆LMK

33. Your turn! Try e-h! SAS ∆CDA ≅ ∆BDA

34. ASA ∆RST ≅ ∆UVT

35. AAS ∆RUT ≅ ∆RST

36. SAS ∆FJH ≅ ∆GHJ

37. A M R C W G MG ≅ AC

38. D X G K Y Z YZ ≅ DK

39. D A E F B C ∠B ≅ ∠E or ∠C ≅ ∠F

40. ASSIGNMENT: “Swimming through triangles” worksheet, both sides (Pages 3 – 4)

41. Warm Up

43. PROOFS! Lesson 4.4

44. TS ≅ TS Given Given Reflexive ∆RST ≅ ∆UTS SSS

45. US ≅ US Given Given Def’n of angle bisector ∠RSU ≅ ∠TSU Reflexive SAS ∆RSU ≅ ∆TSU

46. Your Turn…

47. BD ≅ BD Given Given Reflexive SSS ∆ABD ≅ ∆CBD CPCTC ∠A ≅ ∠C

48. DF ≅ DF DG ≅ FE Given Given Reflexive AIA ≅↔ || lines ∠EDF ≅ ∠GFD AAS ∆EDF ≅ ∆GFD CPCTC

49. BC ≅ BC Given Given Reflexive HL ∆BAC ≅ ∆BDC CPCTC ∠A ≅ ∠D

50. BC || AD BD ≅ BD BC ≅ AD Your Turn… Given Given Reflexive AIA ≅↔ || lines ∠CBD ≅ ∠ADB ∆ABD ≅ ∆CDB SAS