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# Chapter 4 Congruent Triangles

Chapter 4 Congruent Triangles. Identify the corresponding parts of congruent figures Prove two triangles are congruent Apply the theorems and corollaries about isosceles triangles. 4.1 Congruent Figures. Objectives Identify the corresponding parts of congruent figures.

## Chapter 4 Congruent Triangles

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1. Chapter 4Congruent Triangles • Identify the corresponding parts of congruent figures • Prove two triangles are congruent • Apply the theorems and corollaries about isosceles triangles

2. 4.1 Congruent Figures Objectives • Identify the corresponding parts of congruent figures

3. What we already know… • Congruent Segments • Same length • Congruent Angles • Same degree measure

4. F E Congruent Figures Exactly the same size and shape. Don’t ASSume ! C B A D

5. Two figures are congruent if corresponding vertices can be matched up so that: 1. All corresponding sides are congruent 2. All corresponding angles are congruent. Definition of Congruency

6. What does corresponding mean again? • Matching • In the same position

7. Volunteer • Draw a large scalene triangle (with a ruler) • Cut out two congruent triangles that are the same • Label the Vertices A, B, C and D, E, F

8. You can slide and rotate the triangles around so that they MATCH up perfectly. ABC DEF A E C B F D

9. The order in which you name the triangles matters ! ABC DEF A E C B F D

10. Based on the definition of congruency…. • Three pairs of corresponding sides • Three pairs of corresponding angles 1.  A   D 1. AB  DE 2.  B   E 2. BC  EF 3.  C   F 3. CA  FD

11. It is not practical to cut out and move the triangles around

12.  ABC   XYZ • Means that the letters X and A, which appear first, name corresponding vertices and that •  X   A. • The letters Y and B come next, so •  Y   B and • XY  AB

13. CAUTION !! Don't ASSume • If the diagram doesn’t show the markings or • You don’t have a reason • Shared sides, shared angles, vertical angles, parallel lines

14. White Boards • Suppose  TIM   BER IM  ___

15. White Boards • Suppose  TIM   BER IM  ER , Why ?

16. White Boards • Corresponding Parts of Congruent Triangles are Congruent

17. White Boards • Suppose  TIM   BER ___   R

18. White Boards • Suppose  TIM   BER  M   R, Why?

19. White Boards • Corresponding Parts of Congruent Triangles are Congruent

20. White Boards • Suppose  TIM   BER  MTI   ____

21. White Boards • Suppose  TIM   BER  MTI   RBE

22. White Boards • If  ABC   XYZ m  B = 80 m  C = 50 Name four congruent angles

23. White Boards • If  ABC   XYZ m  B = 80 m  C = 50  A,  C ,  X,  Z

24. White Boards • If  ABC   XYZ Write six congruences that must be correct

25. White Boards • If  ABC   XYZ 1.  A   X 1. AB  XY 2.  B   Y 2. BC  YZ 3.  C   Z 3. CA  ZX

26. Remote time • Always • Sometimes • Never • I don’t know

27. A. AlwaysB. SometimesC. NeverD. I don’t know • An acute triangle is __________ congruent to an obtuse triangle.

28. A. AlwaysB. SometimesC. NeverD. I don’t know • A polygon is __________ congruent to itself.

29. A. AlwaysB. SometimesC. NeverD. I don’t know • A right triangle is ___________ congruent to another right triangle.

30. A. AlwaysB. SometimesC. NeverD. I don’t know • If  ABC   XYZ,  A is ____________ congruent to  Y.

31. A. AlwaysB. SometimesC. NeverD. I don’t know • If  ABC   XYZ,  B is ____________ congruent to  Y.

32. A. AlwaysB. SometimesC. NeverD. I don’t know • If  ABC   XYZ, AB is ____________ congruent to ZY.

33. 4.2 Some Ways to Prove Triangles Congruent Objectives • Learn about ways to prove triangles are congruent

34. Don’t ASSume • Triangles cannot be assumed to be congruent because they “look” congruent. and • It’s not practical to cut them out and match them up so,

35. We must show 6 congruent pairs • 3 angle pairs and • 3 pairs of sides

36. WOW • That’s a lot of work Isn't there a shortcut ?

37. Spaghetti Experiment • Using a small amount of playdough as your “points” put together a 5 inch, 3 inch and 2.5 inch piece of spaghetti to forma triangle. • Be careful, IT’S SPAGHETTI, and it will break.

38. Compare your spaghetti triangle to your neighbors • Compare your spaghetti triangle to my spaghetti triangle. What do you notice ?

39. We are lucky….. • There is a shortcut • We don’t have to show • ALL pairs of angles are congruent and • ALL pairs of sides are congruent

40. If three sides of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SSS Postulate E B C D A F

41. Patty Paper Practice 5 inches 3 inches 2.5 inches

42. Volunteer

43. If two sides and the included angle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS Postulate E B C D F

44. If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. ASA Postulate E B C D A F

45. The order of the letters MEAN something • Is SAS the same as SSA or A\$\$ ?

46. Construction 2 Given an angle, construct a congruent angle. Given: Construct: Steps:

47. Construction 3 Given an angle, construct the bisector of the angle Given: Construct: Steps:

48. CAUTION !! Don't ASSume • If the diagram doesn’t show the markings or • You don’t have a reason • Shared sides, shared angles, vertical angles, parallel lines

49. Remote Time Can the two triangles be proved congruent? If so, what postulate can be used? A. SSS Postulate • SAS Postulate • ASA Postulate • Cannot be proved congruent • I don’t know

50. A. SSS PostulateB. SAS PostulateC. ASA PostulateD. Cannot be proved congruentE. I don’t know

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