1. I have faith in myself I have faith in my teachers I will accept my duties and responsibilities I will respect others and seek their respect I have self respect I have self control I can learn if I study hard I will learn because I will study hard I love myself And loving myself I'll be myself And know myself` I am the one who is talking Balance Order Harmony Reciprocity Truth Justice Righteousness Look around you And behold us in our greatness Greatness is a Panther Possibility And you can make it yours!!!!!!!!!!! SCHOOL CREED

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6. HOMEWORK www.mrhillsclass.com

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10. 4-6: Page 219-220, 9-30Homework Practice Quiz Triangle ABC is Isosceles. If angle A measures 45 and BC CD, What is the measure of angle D? A B C 45 Name ___________________________ Period ____ Answer: _______ Why? ____________________________________________ ____________________________________________ D

11. 4-6: Page 219-220, 9-30Homework Quiz Triangle ABC is Equilateral, with BC CD. What is the measure of angle D? A B C Name ___________________________ Period ____ Answer: _______ Why? ____________________________________________ ____________________________________________ D

12. 4-7: Page 224-225, 10-24Homework Practice Quiz What are the coordinates for point B? A B C 45 Name ___________________________ Period ____ Answer: _______ Why? ____________________________________________ ____________________________________________ (2a, 0) (0, 0) (?, ?) 45

13. 4-7: Page 224-225, 10-24Homework Quiz What are the coordinates for point B? A B C 60 Name ___________________________ Period ____ Answer: _______ Why? ____________________________________________ ____________________________________________ (2a, 0) (0, 0) (?, ?) 60

14. Page 186 3 rd Angle Theorem If 2 angles of a triangle are congruent, then the 3 rd angle of both triangles are also congruent A B C 48 D E F 89 If A + B + C = 180, and D + E + F = 180 A + B = D + E C = F 3 rd Angle

15. Page 215 Right Triangle Congruency The Theorems LL, HA, LA and Postulate HL are also used to prove right triangles to be congruent LL (SAS) [or] a 2 + b 2 = c 2 HA (AAS) (ASA) (3 rd Angle Theorem) LA (ASA) HL Postulate (a 2 + b 2 = c 2 )

17. 5-2: Page 252-253, 17-50Homework Practice Quiz Indicate which statement(s) below are true: A. Angle D > Angle A + Angle B B. Angle D > Angle B C. Angle D = Angle A + Angle B D. Angle A = Angle B A B C 45 Name ___________________________ Period ____ Answer: _______ Why? ____________________________________________ ____________________________________________ D

18. 5-2: Page 252-253, 17-50Homework Quiz Explain why choice A below is false. Use Mathematics. A. Angle D > Angle A + Angle B A B C 45 Name ___________________________ Period ____ Why? ____________________________________________ ____________________________________________ D

19. 5-2: Page 252-253, 17-50  Opposite Side Theorem & Angle Sum Theorem (Page 253) Exterior Angle Inequality Theorem

20. 5-2: Page 252-253, 17-50 Exterior Angle Inequality Theorem LKJ LJK Isosceles  Theorem LKJ = LJK Def. of angles m 1 > m LKJ Exterior Inequality Th. m 1 > m LJK Substitution 6. m LJK > m 2 6. Exterior Inequality Th. 7. m 1 > m 2 7. Transitive Property GivenJM JL, JL KL

21. 5-2: Page 252-253, 17-50  Opposite Side Theorem PR PQ, QR > QPGiven m P > m R  Opposite Side Theorem Q R  Isosceles  Theorem Q = R  Def. of m P > m Q Substitution

22. 5-4: Page 264-265, 14-44Homework Practice Quiz In the illustration below, AB BC. State why BC + CD > BD A B C Name ___________________________ Period ____ Answer: ____________________________________________ ____________________________________________ D

23. 5-4: Page 264-265, 14-44 Homework Quiz In the illustration below, AB BC. State why AB + CD > BD A B C Name ___________________________ Period ____ Answer: ____________________________________________ ____________________________________________ D

24. 5-4: Page 264-265, 14-44  Inequality Theorem

25. 5-4: Page 264-265, 14-44  Inequality Theorem B ABC Given AB AC Def. of Isosceles  AB = ACDefinition of AD + AC > CD  Inequality Theorem AD + AB > CD Substitution

26. 5-4: Page 264-265, 14-44  Inequality Theorem HE EG Given Definition of EG + FG > EF Substitution HE = EG  Inequality Theorem HE + FG > EF

27. 5-4: Page 264-265, 14-44  Inequality Theorem D

28. 5-5: Page 271-272, 10-23Homework Practice Quiz In the illustration below, write an inequality to describe the possible values for x. A B Name ___________________________ Period ____ Answer: ____________________________________________ C 36 o 5253 o 8 X + 1 (X + 3) 10 units

29. 5-5: Page 271-272, 10-23Homework Quiz In the illustration below, write an inequality to describe the possible values for x. A B Name ___________________________ Period ____ Answer: ____________________________________________ C 36 o 5253 o 8 X + 2 (X + 3) (X + 4)

30. 5-5: Page 271-272, 10-23 SAS Inequality Theorem (Hinge) and SSS Inequality Theorem 8 (58 o )

31. 5-5: Page 271-272, 10-23

32. (Duplicate page) 61 o SAS Inequality Theorem (Hinge)

33. 5-5: Page 271-272, 10-23 SAS Inequality Theorem (Hinge)  ABC, AB CD Given BD Reflexive Property m 1 > m 2 Exterior Inequality BC > ADSAS Inequality

34. 5-5: Page 271-272, 10-23 SSS Inequality Theorem PQ RS Given QS Reflexive Property QR < PSGiven m 3 < m 1SSS Inequality

35. 5-5: Page 271-272, 10-23 SAS Inequality Theorem (Hinge)

36. 5-5: Page 271-272, 10-23 SAS Inequality Theorem (Hinge)

40. Ratio: (Page 282) A comparison of two quantities abab Proportion: (Page 283) Equivalent fractions set equal to each other. abab cdcd = Cross Products: (page 283) Cross Multiplication: 3434 = 6x6x Extremes/Means: (pages 283) 3434 = 6868

41. Chapter 6 & 7 Vocabulary Similar Polygons: Polygons with the same shape but different in size are proportional. (Page 289) AB CD EF G H Scale Factor: The ratio resulting in the comparison of two lengths 4 8 4848 = … a scale factor of 1212 (we simply reduce) AD CD = EH GH 8 16 4848 = 8 16 64 = 64

42. Chapter 6 & 7 Vocabulary Angle Angle (AA) Postulate: If two angles of 2 triangles are congruent, then the triangles are similar. (Page 298) 3 rd Angle Theorem and Angle Sum Theorem

43. Chapter 6 & 7 Vocabulary SSS Similarity: If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. (Page 299) 3 4 5 6 8 10 3434 = 6868 3636 = 4848

44. Chapter 6 & 7 Vocabulary SAS Similarity: If the measures of 2 sides of a triangle are proportional to 2 sides of another triangle, and the included angles are congruent, then the triangles are similar. (Page 299) 4 5 8 10 4545 = 8 10

45. Chapter 6 & 7 Vocabulary Triangle Proportionality Theorem and it’s Converse: A line parallel to another side of a triangle intersecting the same triangle separates the triangle into proportional segments. (Page 307, 308) 8 10 6 8 5 3 3 5 3333 = 5555

46.  Mid-segment Theorem: (Page 308) A mid-segment of a triangle is parallel to one side of said triangle and has a length half that of the side to which it is parallel. 16 10 6 6 8 Chapter 6 & 7 Vocabulary

47. Proportional Perimeters Theorem: If 2 triangles are similar, then the measures of their perimeters are proportional to the measures of the corresponding sides. (Page 316) 8 10 6 5 3 6 24 = 3 12 4 72 = 72

48. Chapter 6 & 7 Vocabulary Similar Triangle Theorem #1: If 2 triangles are similar, then the measures of their corresponding altitudes are proportional to the measures of their corresponding sides. (Page 317) = 6 = 6

49. Chapter 6 & 7 Vocabulary Similar Triangle Theorem #2: If 2 triangles are similar, then the measures of their corresponding angle bisectors are proportional to the measures of their corresponding sides. (Page 317) A C B D E GF H AD EH = AB EF

50. Chapter 6 & 7 Vocabulary Similar Triangle Theorem #3: If 2 triangles are similar, then the measures of their corresponding medians are proportional to the measures of their corresponding sides. (Page 317) A C B D E GF H AD EH = AC EG

51. Chapter 6 & 7 Vocabulary Iteration: Repeating the same process over and over again. (Page 317)

52. Chapter 6 & 7 Vocabulary Fractal: A Geometric figure that is created using iteration. (Page 325)

53. Chapter 6 & 7 Vocabulary Self Similar: Where we observe smaller portions of a shape or figure to possess the same geometric characteristics as the original figure. (Page 325)

54. Chapter 6 & 7 Vocabulary Pythagorean Theorem: a 2 + b 2 = c 2 (Page 350) Pythagorean Triple: (Page 352) 3 4 5 5 12 13 Justification: 9 + 16 = 25 25 + 144 = 169 4 + 4 = 8 4 + 12 = 16 (45-45-90) (30-60-90)

56. 40 o 63 o 117 o 31.5 o 55 o < 65 o

57. 9 > 5 6x = x + 9 5x = 9 x = 9 5

58. 2 = y 8 16 8y = 32 y = 4

59. 8 = 6 5 x 8x = 30 x = 3.75 3 – 4 – 5 S.R.T. 15 = 39 10 X + 10 15x + 150 = 390 15x = 240 x = 16 39 + 52 + 26 = 117 5 – 12 – 13 S.R.T.

64. 30 – 60 – 90 S.R.T. 45 – 45 – 90 S.R.T. 180(n – 2) n = 6

65. 5 – 12 – 13 S.R.T. 180(n – 2) n = 8

66. 180(n – 2) n = 5 180(n – 2) = 135 o n n = 8 180 o – 135 o = 45 o 180(n – 2) = 108 o n n = 5 180 o – 108 o = 72 o Alternate Interior Angles are congruent 4x + 3 = 5x – 3 – x = – 6 x = 6 (4x + 3) (5x - 3)

67. 180(n – 2) = 120 o n n = 6 180 o – 120 o = 60 o 4x + 3 = 5x – 3 – x = – 6 x = 6 Opposite sides of parallelograms are congruent [or] 360 o = 60 o 6 Also works for #’s 23, 24

68. Diagonals of rectangles bisect each other Consecutive Interior angles of parallelograms are supplementary 1 to 3 y to 15 ……….or 15/3 = 5 or simply, … What number multiplied by 3 is equal to 15? 1 to 3 5 to (3)(5)…….or 3(5) = 15

69. Estimations

70. Answer: 1024 P-value: 68% Correct 21020 10264 What is the sum of the numbers in the 10 th row?

75. STOP

76. 6-1: Page 285-286, 12-35Homework Practice Quiz The triangle shown below has angles A, B, C with a ratio of 1:2:3 respectively. What are the measures of each angle? B C Name ___________________________ Period ____ Answer: ____________________________________________ A 1 + 2 + 3 = 6 equal parts 180 o /6 = 30 o per part Angle A = 30 o (1) = 30 o Angle B = 30 o (2) = 60 o Angle C = 30 o (3) = 90 o

77. 6-1: Page 285-286, 12-35Practice Quiz A salesman sold 720 computers during the months of January, February and March at a ratio of 2:3:4 respectively. How many computers did he sell during each month? Name ___________________________ Period ____ Answer: ____________________________________________ January - February - March -

78. 6-1: Page 285-286, 12-35

79. 6-1: Page 285-286Ratio & Proportion Practice Quiz Solve for x. Show your work Name ___________________________ Period ____ Answer: ____________________________________________ x + 10 = 25 18 30 30x + 300 = 450 -300 -300 30x = 150 30 x = 5

80. 6-1: Page 285-286Ratio & Proportion Quiz Solve for x. Show your work Name ___________________________ Period ____ Answer: ____________________________________________ x + 34 = 65 30 78

81. STOP

82. Geometry Agenda January 2 nd, 2008 1.Bell Ringer; Study Guide – Start Page 154, #32 2.Chapter 6 HW Review; page 293-295, 11-48, 2 nd Run 3.Chapter 6 HW Quiz; page 293-295, 11-48 4.[or] 5.Chapter 6 Test 6.Chapter 7 Test

83. 6-2: Page 293-295, 11-48Homework Practice Quiz The triangles ABC and DEF shown below are similar. Determine the value of x. B C Name ___________________________ Period ____ Answer: ____________________________________________ A 5 = 1 x x = E F D 5 1 10 2 x 5x = x =

84. 6-2: Page 293-295, 11-48Homework Quiz The triangles ABC and DEF shown below are similar. Determine the value of x. B C Name ___________________________ Period ____ Answer: ____________________________________________ A E F D 45 21 x + 25 28 75 x

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86. 6-2: Page 293-295, 11-48

87. 6-2: Page 293-295, Questions 40-47 A E GF A B D C 12 26 14 8 7.5 Inferred by the 4.5 in the original image

88. STOP

89. 6-3: Page 302-304, 10-35Homework Practice Quiz AB is parallel to DE. A E, B D and ACB ECD. Solve for x. B C Name ___________________________ Period ____ Answer: ____________________________________________ A E D 9 6 x x + 1 6 = x 9 x + 1 6x + 6 = 9x -3x = -6 x = 2

90. 6-3: Page 302-304, 10-35Homework Quiz AB is parallel to DE. A E, B D and ACB ECD. Solve for x. B C Name ___________________________ Period ____ Answer: ____________________________________________ A E D 12 x + 6 x x + 1

91. 6-3: Page 302-304, 10-35

92. STOP

95. 6-4: Page 312-314, 14-37

96. STOP

99. 6-5: Page 320-322; 10-29, 32, 35, 36

100. STOP

103. 6-6: Page 328-329; 11-38

104. STOP

108. 7-2: Page 354-355; 12-44

109. STOP

110. 30 o