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

HOMEWORK

HOMEWORK

HOMEWORK

HOMEWORK

4-6: Page , 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

4-6: Page , 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

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

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

Page 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

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 )

5-2: Page , 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

5-2: Page , 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

5-2: Page ,  Opposite Side Theorem & Angle Sum Theorem (Page 253) Exterior Angle Inequality Theorem

5-2: Page , 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

5-2: Page ,  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

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

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

5-4: Page ,  Inequality Theorem

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

5-4: Page ,  Inequality Theorem HE EG Given Definition of EG + FG > EF Substitution HE = EG  Inequality Theorem HE + FG > EF

5-4: Page ,  Inequality Theorem D

5-5: Page , 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

5-5: Page , 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)

5-5: Page , SAS Inequality Theorem (Hinge) and SSS Inequality Theorem 8 (58 o )

5-5: Page , 10-23

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

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

5-5: Page , SSS Inequality Theorem PQ RS Given QS Reflexive Property QR < PSGiven m 3 < m 1SSS Inequality

5-5: Page , SAS Inequality Theorem (Hinge)

5-5: Page , SAS Inequality Theorem (Hinge)

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

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 = … a scale factor of 1212 (we simply reduce) AD CD = EH GH = = 64

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

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) = = 4848

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) = 8 10

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) = 5555

 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 Chapter 6 & 7 Vocabulary

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) = = 72

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

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

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

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

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

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)

Chapter 6 & 7 Vocabulary Pythagorean Theorem: a 2 + b 2 = c 2 (Page 350) Pythagorean Triple: (Page 352) Justification: = = = = 16 ( ) ( )

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

9 > 5 6x = x + 9 5x = 9 x = 9 5

2 = y y = 32 y = 4

8 = 6 5 x 8x = 30 x = – 4 – 5 S.R.T. 15 = X x = x = 240 x = = – 12 – 13 S.R.T.

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

5 – 12 – 13 S.R.T. 180(n – 2) n = 8

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

180(n – 2) = 120 o n n = 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

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

Estimations

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

STOP

6-1: Page , 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 = 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

6-1: Page , 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 -

6-1: Page , 12-35

6-1: Page Ratio & Proportion Practice Quiz Solve for x. Show your work Name ___________________________ Period ____ Answer: ____________________________________________ x + 10 = x = x = x = 5

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

STOP

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

6-2: Page , 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 x 5x = x =

6-2: Page , 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 x x

6-2: Page , 11-48

6-2: Page , Questions A E GF A B D C Inferred by the 4.5 in the original image

STOP

6-3: Page , 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 = x 9 x + 1 6x + 6 = 9x -3x = -6 x = 2

6-3: Page , 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

6-3: Page , 10-35

STOP

6-4: Page , 14-37

STOP

6-5: Page ; 10-29, 32, 35, 36

STOP

6-6: Page ; 11-38

STOP

7-2: Page ; 12-44

STOP

30 o