5. Pre-Algebra 5-6 Congruence 5-6 Congruence Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

6. Pre-Algebra 5-6 Congruence Learning Goal Assignment Learn to use properties of congruent figures to solve problems.

7. Pre-Algebra 5-6 Congruence correspondence Vocabulary

8. Pre-Algebra 5-6 Congruence A correspondence is a way of matching up two sets of objects. If two polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices in the second polygon are written in order of correspondence with the first polygon.

9. Pre-Algebra 5-6 Congruence Additional Example 1A: Writing Congruent Statements The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence. A  Q, so A corresponds to Q. B  R, so B corresponds to R. C  P, so C corresponds to P. The congruence statement is triangle ABC  triangle QRP. Write a congruence statement for the pair of polygons.

10. Pre-Algebra 5-6 Congruence Try This: Example 1A The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence. A  S, so A corresponds to S. B  T, so B corresponds to T. C  Q, so C corresponds to Q. The congruence statement is trapezoid ABCD  trapezoid STQR. A B C D Q R ST D  R, so D corresponds to R. | || ||| |||| | || ||| |||| Write a congruence statement for the pair of polygons. 60° 120° 60° 120°

11. Pre-Algebra 5-6 Congruence Pre-Algebra HW Page 741 #1-10

12. Pre-Algebra 5-6 Congruence Additional Example 1B: Writing Congruent Statements The vertices in the first pentagon are written in order around the pentagon starting at any vertex. D  M, so D corresponds to M. E  N, so E corresponds to N. F  O, so F corresponds to O. The congruence statement is pentagon DEFGH  pentagon MNOPQ. G  P, so G corresponds to P. H  Q, so H corresponds to Q. Write a congruence statement for the pair of polygons.

13. Pre-Algebra 5-6 Congruence Try This: Example 1B The vertices in the first hexagon are written in order around the hexagon starting at any vertex. A  M, so A corresponds to M. B  N, so B corresponds to N. C  O, so C corresponds to O. The congruence statement is hexagon ABCDEF  hexagon MNOPQL. D  P, so D corresponds to P. E  Q, so E corresponds to Q. A B C D E F N O P Q L M F  L, so F corresponds to L. Write a congruence statement for the pair of polygons. 140° 110° 140° 110°

14. Pre-Algebra 5-6 Congruence Additional Example 2A: Using Congruence Relationships to Find Unknown Values In the figure, quadrilateral VWXY  quadrilateral JKLM. a = 16 –8 –8 Subtract 8 from both sides. A. Find a. a + 8 = 24 WX  KL

15. Pre-Algebra 5-6 Congruence Try This: Example 2A In the figure, quadrilateral JIHK  quadrilateral QRST. A. Find a. 3a3a 4b° 6 30° Q 120° R S H I J K 3a = 6 3 3 a = 2 c + 10° T 3a = 6 IH  RS Divide both sides by 3.

16. Pre-Algebra 5-6 Congruence In the figure, quadrilateral VWXY  quadrilateral JKLM. 6 6 6b = 30 Divide both sides by 6. B. Find b. 6b = 30 ML  YX b = 5 Additional Example 2B: Using Congruence Relationships to Find Unknown Values

17. Pre-Algebra 5-6 Congruence B. Find b. Divide both sides by 4. 4 4 4b = 120 b = 30° 4b = 120 H  S Try This: Example 2B In the figure, quadrilateral JIHK  quadrilateral QRST. 3a3a 4b° 6 30° Q 120° R S H I J K c + 10° T

18. Pre-Algebra 5-6 Congruence 5c = 85 J  V 5 5 5c = 85 Divide both sides by 5. C. Find c. c = 17 In the figure, quadrilateral VWXY  quadrilateral JKLM. Additional Example 2C: Using Congruence Relationships to Find Unknown Values

19. Pre-Algebra 5-6 Congruence C. Find c. c = 20° Subtract 10 from both sides. –10 c + 10 = 30 K  T Try This: Example 2C 3a3a 4b° 6 30° 90° Q 120° 90° R S H I J K T c + 10° In the figure, quadrilateral JIHK  quadrilateral QRST.

21. Pre-Algebra 5-6 Congruence 5-7 Transformations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

22. 5-7 Learning Goal Assignment Learn to transform plane figures using translations, rotations, and reflections.

23. Vocabulary transformation translation rotation center of rotation reflection image

24. When you are on an amusement park ride, you are undergoing a transformation. Ferris wheels and merry-go-rounds are rotations. Free fall rides and water slides are translations. Translations, rotations, and reflections are type of transformations.

25. The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

26. Additional Example 1A & 1B: Identifying Transformations Identify each as a translation, rotation, reflection, or none of these. A. B. reflection rotation

27. Try This: Example 1A & 1B Identify each as a translation, rotation, reflection, or none of these. A B C A. B. A B C D A’ B’ C’ D’ translation reflection A’A’ B’B’ C’C’

28. Additional Example 1C & 1D: Identifying Transformations Identify each as a translation, rotation, reflection, or none of these. C. D. none of the thesetranslation

29. Identify each as a translation, rotation, reflection, or none of these. B C D E F C. D. A A’A’ B’B’ C’C’ D’D’ F’F’ E’E’ rotation none of these Try This: Example 1C & 1D

30. Additional Example 2A: Drawing Transformations Draw the image of the triangle after the transformation. A B C A. Translation along AB so that A’ coincides with B A’ B’ C’

31. Try This: Example 2A Draw the image of the polygon after the transformation. A B C D E F A’ B’ C’ D’ E’ F’ A. Translation along DE so that E’ coincides with D

32. Additional Example 2B: Drawing Transformations Draw the image of the triangle after the transformation. A B C B. Reflection across BC. A’ B’ C’

33. Try This: Example 2B Draw the image of the polygon after the transformation. A B C D E F B. Reflection across CD. A’ B’ C’ D’ E’ F’

34. Draw the image of the triangle after the transformation. A B C C. 90° clockwise rotation around point B A’ B’ C’ Additional Example 2C: Drawing Transformations

35. Draw the image of the polygon after the transformation. A B C D E F C’ A’ B’ D’ E’F’ C. 90° counterclockwise rotation around point C Try This: Example 2C

36. Additional Example 3A: Graphing Transformations Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation. A. 180° counterclockwise rotation around (0, 0)

37. Try This: Example 3A Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. A. 180° clockwise rotation around (0, 0) x y –2 2

38. Additional Example 3B: Graphing Transformations Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation. B. Translation 5 units left

39. B. Translation 10 units left Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. Try This: Example 3B x y –2 2

40. Additional Example 3C: Graphing Transformations Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation. C. Reflection across the x-axis

41. Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. Try This: Example 3C x y –2 2