Download Geometry Chapter 7 Notes 10-11

Date: _________________________
AIMS Practice Problems
6
1. If the pattern below continues, what
will be the 8th term?
4. If RS = 50.1 and QS = 82.9, find QR.
2.2, 2.5, 2.8, 3.1, 3.4, …
A.
B.
C.
D.
4.0
4.1
4.2
4.3
2. Determine the relationship between
the two equations
yx
 4 y  4  4x
Q
A.
B.
C.
D.
R
S
32.8
133
50.1
22.8
5. What is the slope of the line in the figure
below?
5
4
A.
Parallel
B.
Perpendicular
C.
Coincide
D.
Intersecting but not
perpendicular
3
2
1
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
3. The set {-3, 0, 6, 12} is a
subset of
A. Whole Numbers
B.
Integers
C. Natural Numbers
D. Irrational Numbers
A. 4
B. -4
C.
1
4
D. 
1
4
2
3
4
5
NOTES: 7.1 Ratios and Proportions
Proportion - an equation that states that two ratios are equal
*To solve: cross multiply and solve.
Solve the proportion.
1.
3 6

x 8
2.
5 15

3 y
3.
x 5

18 6
4.
4 x

9 63
5.
5 y2

3
6
6.
m  2 14

5
10
7.
2
8

7 w2
8.
12
96

7 y2
Ratio and Proportion
Ratio: a comparison of two numbers
*Ratio a to be can be written in three ways
a
b
a :b
a to b
Simplifying ratios:
make sure units are the same (if not convert)
simplify the fraction to lowest terms
Simplify the ratio (like you would simply FRACTIONS)
1.
60cm : 200cm
2.
3 ft
18 ft
3.
12m
10m
4.
2months
8months
Use the diagram to answer the following questions.
A
B C
1 2 3 4
5 6
D
E
7 8 9 10 11 12 13 14
Use the number line to find the given ratio.
1.
AB : BC
2.
BD : DE
3.
AC : AE
4.
BD : BE
5.
AD : AE
6.
EC : CA
Using ratios
1. In the diagram below AB : BC is 4 :1 and AC  30
Find AB and BC
A
B
C
2. FG : GH is 4 : 3 , FH  56
Find FG and GH
3. The perimeter of a rectangle is 80 ft .
The ratio of the length to width is 7 : 3
Find the length and the width.
4. In the diagram EF : FG is 2 :1 and EG  24
Find EF and FG
E
F
G
5. The perimeter of a rectangle is168 ft .
The ratio of the length to width is 4 : 3 .
Find the length and the width of the rectangle
Assignment: Section 7.1
Page 361- 363 # 25-45 NOT 27, and 55
Date: _________________________
AIMS Practice Problems
6
1. The square root of 31 belongs to
which subset?
A.
B.
C.
D.
Natural Numbers
Counting Numbers
Rational Numbers
Irrational Numbers
2. Which value is closest to
A.
B.
C.
D.
?
A.
B.
C.
D.
x=5
x = 18
x = -18
x = -5
8.1
9.2
10.8
12.1
3. Evaluate 3x - 4y for the values
x = -4 and y = -2.
A.
B.
C.
D.
4. Which of the following values of
x makes the proportion below true?
-20
-4
4
20
5. Which of the following is an
example of dependent events?
A. flipping a fair coin twice and getting
tails both times
B. choosing the starting player line-up
for a basketball game
C. choosing two cards from a stack of
colored cards, with replacement,
and both cards are blue
D. rolling a 6-sided die 2 times and
getting a 5 both times
NOTES: 7.2 Similar Polygons
Polygons are similar when
1. corresponding (same place) angles are
congruent (the same)
2. corresponding (same place) sides are
proportional (reduce to same fraction)
is the symbol for similar
ABCD EFGH . List corresponding angles and ratios of
corresponding sides.
C
G
B
F
A
D
E
H
Statement of Proportionality
Corresponding Angles
(Ratio of Corresponding Sides)
Scale Factor: the SIMPLIFIED ratio (fraction) of the
lengths of two corresponding sides of a similar polygon
** if all fractions reduce to the same thing, they are not
only similar, but this is also your scale factor.
In the diagram PRQ
STU
T
R
16
8
20
S
10
P
15
12
U
Q
1. List all pairs of congruent angles.
2. Write the statement of proportionality.
3. Check that the ratios of the sides are equal (use the
ratios of sides from above, only use the numbers, not
the letters)
4. What is the scale factor of the above figures?
Determine whether the polygons are similar.

are corresponding angles  ?

are corresponding sides proportional?
If similar, write a statement of similarity ( ABC XYZ ) a
AB BC CA
statement of proportionality (


) and find the
XY YZ ZX
scale factor.
H
K
1.
9
12
16
G
M
2.
12
L
20
12
N
J
15
P
10
S
9
T
6
Q
U
V
R
E
3. Y
12
18
6
9
Z
12
X
F
D
8
Solving Similar Polygons

Solve for variables of similar polygons by using
corresponding sides to set up a proportion.
Solve for the variables.
1.
RST
GHJ
S
H
15
10
9
8
T
R
x
2.
PQR
J
G
y
STU
T
Q
7
14
x
S
P
9
16
y
R
U
3.
ABCD
WXYZ
W
A
X
B
b
4
D
4.
C
6
XYZ
Z
Y
12
DEF
E
Y
27
x
21
28
Z
F
D
20
X
Assignment: Section 7.2
Page 368 – 371 # 8 – 26 even
y
Date: _________________________
AIMS Practice Problems
6
1. Simplify: ( x  4)( x  3)
A.
B.
C.
D.
2. If RS = 41.7 and QS = 77.8, find QR.
x 2  x  12
x 2  7 x  12
x2  1
Q
A.
B.
C.
D.
x 1
R
S
36.1
26.1
119.5
41.7
1
3. Which of the graphs below correctly represents the equation y   x  3 ?
2
A.
B.
-5
-4
-3
-2
5
5
4
4
3
3
2
2
1
1
-1
C.
1
2
3
4
5
-4
-3
-2
-4
-3
-2
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
D.
5
-5
-5
-1
4
3
3
2
2
1
1
1
2
3
4
5
2
3
4
5
1
2
3
4
5
5
4
-1
1
-5
-4
-3
-2
-1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Review:
Are the polygons similar?
If so, write the similarity statement, the statement of
proportionality and find the scale factor.
Y
B
12
6
2
A
4
8
C
X
16
Solve the proportion.
1.
5 y2

3
6
2.
3 6

x 8
3.
5 15

3 y
4.
m  2 14

5
10
Z
NOTES: 7.3 Showing Triangles are Similar
Angle – Angle (AA)
Angle – Angle Similarity Postulate (AA)
If two angles of one triangle are congruent to two angles of
another triangle, then the two triangles are similar
Y
K
J
L
X
Z
JKL
XYZ
Determine whether the triangles are similar.
If they are, write the similarity statement.

you may need to find the missing angle
measurement. Subtract from 180.
K
1. H
61
G
J
29
L
R
2.
80
T 65
S
M
F
80
L
39
N
Are you given enough information to determine whether
the triangles are similar. If so, write the similarity
statement.

shared angles are 

vertical angles are 
1.
R
M
80
80
T 65
S
R
2.
T
S 48
U
35
L
V
48
3. A
D
B
C
E
N
Using Similar Triangles
Write a similarity statement for the triangles. Then find the
value of x.
1.
H
K
25
x
G
F
40
2.
28
L
T
Q
3
5
x
S
P
3.
C
A
x
B
6
y
R
15
12
2
D
6
E
U
4.
G
6
12
H
4
x
I
5.
S
K
J
16
T
45
8
R
x
U
45
4
V
Assignment: Section 7.3
Page 375 - 376 # 2 – 26 even
Date: _________________________
AIMS Practice Problems
#53
6
1. Draw a labeled diagram for a line
segment.
A.
3. The n th term of the pattern defined in
the table is given by which expression?
2
4
C
B
3 4 5
n
9 16 25 ?
A. 5n
B. n 2
C. n  2
D. n  5
A
B.
A
B
C.
A
B
4. If mCOD = 24 and
mBOC = 20 , then what is the measure
of BOD ?
D.
B
A
B
C
D
O
2. Which of these equations represents a
line passing through (5,3) and ( 5, 3) ?
A.
B.
C.
D.
3
x
5
5
y x
3
y 5
y 3
y
A.
B.
C.
D.
41°
42°
49°
44°
NOTES: 7.4 Showing Triangles are Similar
Side – Side – Side (SSS)
Side – Angle – Side (SAS)
Side – Side – Side Similarity Theorem (SSS)
If the corresponding sides of two triangles are proportional,
then the triangles are similar
Determine if the triangles are similar. If they are, write the
similarity statement and find the scale factor.

start with the shortest sides
R
1.
8
12
T
S
10
M
6
4
L
2. A
N
5
12
6
C
9
B
14
G
6
J
10
H
Side – Angle – Side Similarity Theorem
If an angle of one triangle is congruent to an angle of a
second triangle and the lengths of the sides that include
these angles are proportional, then the triangles are similar.
Determine if the triangles are similar. If so, write the
similarity statement.
D
1.
A
5
3
60
B
2.
3
C
60
5
E
F
L
G
6
8
M
H
J
12
3.
R
D
6 85
85
8
E
N
8
10
S
8
T
F
Similarity in Overlapping Triangles
Show that the overlapping triangles are similar

Separate the triangles and label or mark
EVERYTHING
1.
V
5
4
X
W
10
8
Y
Z
N
2.
40
M
16
P
35
Q
14
L
3.
P
5
3
R
Q
5
3
S
T
Assignment: Section 7.4 Page 382 – 385
# 5 – 9, 15 – 25 ONLY ODD
# 32, 33, 38 – 41
Date: _________________________
AIMS Practice Problems
6
1. Determine the solution to the systems of
equations represented by the following graph.
5
3. If mCOD = 27 and
mDOE = 26 , then what is the
measure of COE ?
4
3
2
C
1
-5
-4
-3 -2
-1
1
2
3
4
D
5
-1
E
-2
O
-3
-4
A.
B.
C.
D.
-5
A.
B.
C.
D.
(0,1)
(1, 0)
(0, 0)
(1, 1)
53°
58°
51°
50°
4. Which is the formula to find the
slope of a line?
2. If RS = 30.4 and QS = 60.4, find QR.
A.
B.
Q
A.
B.
C.
D.
R
30
90.8
20
30.4
S
C.
D.
x2  x1
y2  y1
y y
m 2 1
x2  x1
y  y1
m 2
x2  x1
x x
m 2 1
y2  y1
m
Practice: Determine whether the triangles are similar. If
they are similar, state the similarity postulate or theorem
that justifies your answer.
R
1.
2.
80
R
D
6 85
85
8
T
65
10
8
S
T
S
M
E
F
80
39
L
N
R
3.
4.
R
8
12
T
T
S 48
6
4
U
L
V
48
S
10
M
N
5
N
K
5.
6.
H
40
61
J
29
M
G
16
P
35
Q
14
L
F
L
Find the value of the variable.
7.
8.
NOTES: 7.5 Proportions and Similar Triangles
Triangle Proportionality Theorem:
If a line parallel to one side of a triangle intersects the other
two sides then it divides the two sides proportionally
R
RT RU
TU QS so

TQ US
T
U
Q
S
Find the value of the variable
1. set up the proportion, go from small to big
2. plug in side length values
3. solve for the variable
1.
R
4
x
T
U
12
8
Q
2.
S
R
9
Q
3
S
y
20
P
3.
4
x
10
5
4.
14
y
15
6
Determine if the segments are parallel.

are the RATIOS of the sides EQUAL?
1.
MN GH ?
21
G
M
56
L
2.
48
N
16
H
TS RQ ?
T
21
R
15
S
3.
Q
23
P
17
QR ST ?
P
6
4
R
Q
12
8
S
T
The Midsegment Theorem
The Midsegment Theorem:
The segment connecting the midpoints of two sides of a
triangle is parallel to the third side and is half as long
In ABC , if CD  DA
and CE  EB then
1
DE AB and DE  AB
2
C
D
E
A
B
Find the value of the variable
1.
w
2.
17
x
10
q
3.
4
4.
3
8
p
4
11
14
3
8
11
16
Assignment: Section 7.5
Page 390 – 392
# 3 – 29 odd, 44 – 52 even
6
Date: _________________________
AIMS Practice Problems
1.The endpoints of a line segment are the
points with the coordinates (2,1) and (8,9).
What are the coordinates of the midpoint of
this line segment?
A. (2,3.5)
B. (3,4)
C. (5,5)
D. (4.5,5.5)
2. Which property is demonstrated below?
If A=2c and 2c=D, then A=D.
A. Associative Property
B. Distributive Property
C. Reflexive Property
D. Transitive Property
3. The numbers in the data set below can be
classified as members of which subset of
real numbers?
A.
B.
C.
D.
Integers
Irrational Numbers
Rational Numbers
Whole numbers
4. Paul's first project scores for art were:
96, 87, 84, 96, 100
Which statement is true about the project
scores?
A. The mode is the same as the
median.
B. The median is the same as the
mean.
C. The range is the same as the mode.
D. The mode is the same as the mean.
Review: Determine if the following triangles are similar. If
they are, write the similarity statement.
Y
1.
K
33
L
J
32
Z
R
2.
T
S 60
U
V
60
D
3.
A
3
4
B
5
6
C
3
4. A
F
5
E
8
L
J
110
6
8
K
110
C
10
B
X
5. Solve for the variable
Q
10
y
U
R
36
14
S
T
6. Determine if CD is parallel to EF
B
72
96
D
C
40
30
E
F
Find the value of the variable
7.
8.
x
w
13
40
Assignment - REVIEW: Page 401 – 403 # 1 – 23 ALL