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LESSON 7-1
I can determine whether a dilation is an enlargement, a reduction or congruence transformation
I can determine the scale factor for a given dilation
size
imagepreimage
enlargementreduction
congruent
reduction
3/6 or 0.5
enlargement
6/4 or 1.5
36 mm
44 mm34 mm
C’B’
108 mm
132 mm
102 mm
enlargement
3
A’
A’
B’D’
C’
1/3
reduction
P’(rx, ry)
(-4, 4)
(-2, -6)
(6, 6)
(-2, 1.5)
(-1, -2)
(2.5, -1)
r =image
preimage
4 = 6x
x = 1.5
r =image
preimage
=x
5
x = 3.33
2
3
240 in96 in
180 in
4
240= 0.0167=
1
60
4
240=
x
180 x = 3 in
60 in
60
2= 30
60
2=
x
5 x = 150 in
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7-1 worksheet
ASSIGNMENT
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LESSON 7-2
I can write ratios.
I can use properties of proportions.
quotient
with the same units
a : b or a/b
NOT b : a
females : males
elective : non-elective2 : 3
a : b : c
Cannot be written as a fraction
5
7
8
x
x
x
5x + 7x + 8x = 240
20x = 240
x = 12
60
84
96
2
103
x
xx
2x + 10x + 3x = 180
15x = 180
x = 12
24°
120°36°
7x
3x
7x
3x20x = 140
x = 7
L
W
L = 49
fractions equal
diagonals
4(5) = 10(2)
8y = 72
y = 9
6x = 163.8
x = 27.3
4(2x + 3) = 40
8x + 12 = 40
x = 3.5
3(x – 1) = 4(x + 1)
3x – 3 = 4x + 4
x = -7
length
width
40
9=
16
x40x = 144
x = 3.6
3.6 inches
miles
inches
4
1=
x
3.5x = 14
14 miles
gal
miles
5
120=
x
350x = 14.58333
14.6 gallons
wide
tall
5
3.5=
x
18 x = 25.7143
25.7 inches
5
3.5
?
18
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7-2 worksheet
ASSIGNMENT
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LESSON 7-3
I can identify similar figures.
I can find missing side lengths in similar figures.
shapesize
shapesize
congruent
proportional
congruent
similar
12
8
18
12
15
10
9
6
All = 1.5
Similar, all angles congruent,all sides proportional.
10
5
6
3
8
4
All = 2
Similar, all angles congruent,all sides proportional.
13
x=
14
7
x = 6.5
x
9=
8
12x = 6
10
y=
8
12y = 15
Find x first
18
x=
12
18
x = 27
27
Find y next!
y + 1
24=
12
18
18(y + 1) = 288
18y + 18 = 288
27
y = 15
x = 27, y = 15
11
12
Perimeter = 10 + 11 + 12 = 33
J K
L
M N
L
5
12.510y
2
x
10
x=
5
2
x = 4
12.5
y=
5
2
y = 5
x + 4
2=
3x + 3
3
2(3x + 3) = 3(x + 4)
6x + 6 = 3x + 12
x = 2
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7-3 worksheet
ASSIGNMENT
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LESSON 7-4
I can identify similar triangles.
I can use similar triangles to solve problems.
SSS SAS ASA
AAS HL
similar by SSS~
32
20
40
25
24
15= =
Not similar
36
24
20
18≠
Not similar
18
16
16
14
12.5
11≠ ≠
Similar by AA~
30°60°
ΔMKS ~ ΔQTR
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7-4 worksheet
ASSIGNMENT
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LESSON 7-5
I can use the Triangle Proportionality Theorem to find parts of triangles
I can use the Triangle Midsegment Theorem to find parts of triangles.
I can recognize and use proportions to find relationships between altitudes, angle bisectors and medians of similar triangles.
parallel
proportional
7
21
6
x
721 6
x
= x = 18
12x
6
7=
x = 14
x14
NQ = 26
22
xx + 12
11
22= x = 12
x – 4
x – 6 14
6= x = 7.5
endpointsmidpoints 2 sides
parallelhalf
352
= 17.5X =
R
S T
X
Y
12
RS = 2(12)
= 24
proportional
65 7 x
5
7
6
x= x = 8.4
14
10.5
24
x=
2414 10.5
x
x = 18
x + 2
10
2x + 1
14= x = 3
x
8x + 2
12= x = 4
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7-5 worksheet
ASSIGNMENT
WARM-UPA. Tell whether each pair of triangles is similar or not (yes/no)B. Justify your answer.C. If yes, also write a similarity statement (Ex: ABC ~ ZXY)△ △
40°
PR
S50°D
EF
1. 2.
J
G
H8
79L
M
N
4 5
6
Yes, similar by AA~(all angles are congruent)△SPR ~△EDF
No, not similar9
6
7
4
8
5≠ ≠
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LESSON 7-6
I can solve problems involving relationships between parts of a right triangle and the altitude (height) to its hypotenuse (longest side).
ΔABC
D
A C
D
C B
ΔACD ΔCBD
2
x
x
6
2
x
x
6= 𝑥2=12
𝑥=√12= 3.46
3
x y9 y
x
12
3
x
x
12=
9
y
y
12=
𝑥2=36𝑥=√36
𝑦 2=108𝑦=√108
= 6 = 10.39
2
y z5
z
y
7x
x
2
x
x
5=
2
y
y
7=
5
z
z
7=
x = 3.16 y = 3.74 z = 5.92
2
x
x
6=
2
y
y
4=
4
z
z
6=
x = 3.46 y = 2.83 z = 4.90
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7-6 worksheet
ASSIGNMENT
