i have faith in myself i have faith in my teachers i will accept my duties and responsibilities
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•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
4-6: Page 219-220, 9-30Homework Practice Quiz
Triangle ABC is Isosceles. If angle A measures 45and BC CD, What is the measure of angle D?
A
B
C
45
Name ___________________________ Period ____
Answer: _______Why? ____________________________________________ ____________________________________________
D
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
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
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
Page 1863rd Angle TheoremIf 2 angles of a triangle are congruent, then the 3rd angle of both triangles are also congruent
A
B
C48
D
E
F
48
89 89
If A + B + C = 180, and D + E + F = 180
A + B = D + E
C = F
3rd Angle
Page 215Right Triangle CongruencyThe Theorems LL, HA, LA and Postulate HL arealso used to prove right triangles to be congruent
LL (SAS) [or] a2 + b2 = c2
HA (AAS) (ASA) (3rd Angle Theorem)
LA (ASA)
HL Postulate (a2 + b2 = c2)
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 BC. Angle D = Angle A + Angle B D. Angle A = Angle B
A
B
C
45
Name ___________________________ Period ____
Answer: _______Why? ____________________________________________ ____________________________________________
D
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
5-2: Page 252-253, 17-50
Opposite Side Theorem & Angle Sum Theorem (Page 253)
Exterior Angle Inequality Theorem
5-2: Page 252-253, 17-50Exterior 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 252-253, 17-50
Opposite Side Theorem
PR PQ, QR > QP Given
m P > m R Opposite Side Theorem
Q R Isosceles Theorem
Q = R Def. of
m P > m Q Substitution
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
5-4: Page 264-265, 14-44Homework Quiz
In the illustration below, AB BC. State why AB + CD > BD
A
B
C
Name ___________________________ Period ____
Answer: ____________________________________________ ____________________________________________ ____________________________________________ ____________________________________________
D
5-4: Page 264-265, 14-44
Inequality Theorem
5-4: Page 264-265, 14-44
Inequality Theorem
B ABC Given
AB AC Def. of Isosceles
AB = AC Definition of
AD + AC > CD Inequality Theorem
AD + AB > CD Substitution
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
5-4: Page 264-265, 14-44
Inequality Theorem
D
5-5: Page 271-272, 10-23Homework Practice Quiz
In the illustration below, write an inequality todescribe the possible values for x.
A
B
Name ___________________________ Period ____
Answer: ____________________________________________ ____________________________________________ ____________________________________________
C36
o 5253
o 8
X + 1 (X + 3)
10 units
5-5: Page 271-272, 10-23Homework Quiz
In the illustration below, write an inequality todescribe the possible values for x.
A
B
Name ___________________________ Period ____
Answer: ____________________________________________ ____________________________________________ ____________________________________________
C36
o 5253
o 8
X + 2 (X + 3)
(X + 4)
5-5: Page 271-272, 10-23
SAS Inequality Theorem (Hinge) and SSS Inequality Theorem
8
(58o
)
5-5: Page 271-272, 10-23
5-5: Page 271-272, 10-23(Duplicate page)
61o
61o
SAS Inequality Theorem (Hinge)
5-5: Page 271-272, 10-23
SAS Inequality Theorem (Hinge)
ABC, AB CD Given
BD BD Reflexive Property
m 1 > m 2 Exterior Inequality
BC > AD SAS Inequality
5-5: Page 271-272, 10-23
SSS Inequality Theorem
PQ RS Given
QS QS Reflexive Property
QR < PS Given
m 3 < m 1 SSS Inequality
5-5: Page 271-272, 10-23
SAS Inequality Theorem (Hinge)
5-5: Page 271-272, 10-23
SAS Inequality Theorem (Hinge)
Ratio: (Page 282) A comparison of two quantities ab
Proportion: (Page 283) Equivalent fractions set equal to each other. ab
cd
=
Cross Products: (page 283) Cross Multiplication: 34
= 6x
Extremes/Means: (pages 283) 34
= 68
Chapter 6 & 7 Vocabulary
Similar Polygons: Polygons with the same shape but different in size are proportional. (Page 289)
A B
CD
E F
GH
Scale Factor: The ratio resulting in the comparison of two lengths
48
48
= … a scale factor of 12
(we simply reduce)
ADCD
= EHGH
8
16
48
= 8 16
64 = 64
Chapter 6 & 7 Vocabulary
Angle Angle (AA) Postulate: If two angles of 2 triangles are congruent, then the triangles are similar. (Page 298)
3rd 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)
3
4
5
6
8
10
34
= 6 8
36
= 4 8
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
45
= 8 10
Chapter 6 & 7 Vocabulary
Triangle Proportionality Theorem and it’s Converse:
A line parallel to another side of a triangle intersecting the sametriangle separates the triangle into proportional segments. (Page 307, 308)
8
106
8
53
3 5
33
= 5 5
Mid-segment Theorem: (Page 308)
A mid-segment of a triangle is parallel to one side of said triangleand has a length half that of the side to which it is parallel.
16
106
6 108
Chapter 6 & 7 Vocabulary
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)
8
106
53
624
= 3 12
472 = 72
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #1:
If 2 triangles are similar, then the measures of their correspondingaltitudes 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 correspondingangle bisectors are proportional to the measures of their correspondingsides. (Page 317) A
CBD
E
GFH
ADEH
= ABEF
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #3:
If 2 triangles are similar, then the measures of their correspondingmedians are proportional to the measures of their correspondingsides. (Page 317) A
CBD
E
GFH
ADEH
= ACEG
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: a2 + b2 = c2 (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)
40o
63o 63o 117o
31.5o31.5o
55o < 65
o
9 > 5
6x = x + 9
5x = 9
x = 9 5
2 = y8 16
8y = 32
y = 4
8 = 65 x
8x = 30
x = 3.753 – 4 – 5 S.R.T.
15 = 3910 X + 10
15x + 150 = 390
15x = 240
x = 16
39 + 52 + 26 = 117
5 – 12 – 13 S.R.T.
30 – 60 – 90 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) = 135o
n
n = 8
180o – 135
o = 45
o
180(n – 2) = 108o
n
n = 5
180o – 108
o = 72
o
Alternate Interior Angles are congruent
4x + 3 = 5x – 3– x = – 6 x = 6
(4x + 3)
(5x - 3)
180(n – 2) = 120o
n
n = 6
180o – 120
o = 60
o
4x + 3 = 5x – 3– x = – 6 x = 6
Opposite sides of parallelogramsare congruent
[or]
360o = 60o
6
Also worksfor #’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
2 10 20 20 10 2 64
What is the sum of the numbersin the 10th row?
STOP
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 measuresof each angle?
B
C
Name ___________________________ Period ____
Answer: ____________________________________________ ____________________________________________ ____________________________________________
A
1 + 2 + 3 = 6 equal parts
180o/6 = 30o per part
Angle A = 30o(1) = 30o
Angle B = 30o(2) = 60o
Angle C = 30o(3) = 90o
6-1: Page 285-286, 12-35Practice Quiz
A salesman sold 720 computers during the monthsof January, February and March at a ratio of 2:3:4respectively. How many computers did he sell duringeach month?
Name ___________________________ Period ____
Answer: ____________________________________________ ____________________________________________ ____________________________________________
January -February -March -
6-1: Page 285-286, 12-35
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
30x = 15030 30
x = 5
6-1: Page 285-286Ratio & Proportion Quiz
Solve for x. Show your work
Name ___________________________ Period ____
Answer: ____________________________________________ ____________________________________________ ____________________________________________
x + 34 = 65 30 78
STOP
Geometry Agenda January 2nd , 2008
1. Bell Ringer; Study Guide – Start Page 154, #322. Chapter 6 HW Review; page 293-295, 11-48, 2nd Run3. Chapter 6 HW Quiz; page 293-295, 11-484. [or]5. Chapter 6 Test6. Chapter 7 Test
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
51
10 2
x
5x =x =
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: ____________________________________________ ____________________________________________ ____________________________________________
AE
F
D
4521
x + 25 28
75x
6-2: Page 293-295, 11-48
6-2: Page 293-295, Questions 40-47
A E
G F
AB
D C
12
26
14
87.5
Inferred by the 4.5 in the original image
STOP
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
D9
6
xx + 1
6 = x9 x + 1
6x + 6 = 9x
-3x = -6
x = 2
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
D12
x + 6
xx + 1
6-3: Page 302-304, 10-35
STOP
6-4: Page 312-314, 14-37
STOP
6-5: Page 320-322; 10-29, 32, 35, 36
STOP
6-6: Page 328-329; 11-38
STOP
7-2: Page 354-355; 12-44
STOP
30o
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