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Name:
______
Period _________ 2/17/12 – 3/2/12 G-PreAP
UNIT 12: SIMILARITY
I can define, identify and illustrate the following terms:
Dilation
Scale Factor
Extremes
Means
Similarity Statement
Scale Drawing
Enlargement
Reduction
Ratio
Proportion
Cross products
Indirect measurement
Similarity ratio
Dates, assignments, and quizzes subject to change without advance notice.
Monday
13
12- 4 and 12 – 5
Compositions and
Symmetry
20
Tuesday
Review
12-7
Dilations
28
7-6
Dilations & Similarity in
the Coordinate Plane
7-1
Ratios, Proportions,
and Problem Solving
24
7-3 & 7-4
Triangle Similarity &
Applications
QUIZ 1
7-2
Similar Polygons
No School
Friday
17
TEST 11
22/23
21
27
Block Day
15/16
14
7-5
Proportional
Relationships
29/1
8-1
Geometric Mean
QUIZ 2
Review
2
TEST 12
Friday, 2/17
7-1: Ratio and Proportion
 I can write a ratio.
 I can write a ratio expressing the slope of a line.
 I can solve a linear proportion.
 I can solve a quadratic proportion.
PRACTICE: Pg 458 #8-13, 17-29
Tuesday, 2/21
7-2: Similar Polygons
 I can use the definition of similar polygons to determine if two polygons are similar.
 I can determine the similarity ratio between two polygons.
PRACTICE: Pg 465 #7-20, 27-30
Ratio Problems Worksheet
Wednesday, 2/22 or Thursday, 2/23
 QUIZ 1: 7-1 & 7-2
7-3: Triangle Similarity & 7-4: Applications and Problem Solving
 I can use the triangle similarity theorems to determine if two triangles are similar.
 I can use proportions in similar triangles to solve for missing sides.
 I can use the triangle proportionality theorem and its converse.
 I can use the Triangle Angle Bisector Theorem.
 I can set up and solve problems using properties of similar triangles.
PRACTICE: Pg 475 #11-14, 16, 20-24
Pg 485 #8-20, 25, 28, 32, 34
Friday, 2/24
7-5: Using Proportional Relationships
 I can use proportions to determine if a figure has been dilated.
 I can use ratios to make indirect measurements.
PRACTICE: Pg 491 #18-19, 24-26, 28-29, 34
Proportional Relationships Worksheet
Monday, 2/27
7-6: Dilations & Similarity in the Coordinate Plane
 I can use coordinate proof to prove figures similar.
 I can apply similarity in the coordinate plan.
PRACTICE: Pg 498 #4-7, 11-14, 21-24
Tuesday, 2/28
 QUIZ 2: Similar Triangles (7-3 through 7-6)
Geometric Mean
 I can use geometric mean.
PRACTICE: Geometric Mean Worksheet
Wednesday, 2/29 or Thursday, 3/1
Review
 Test 12: Similarity
 I can use ratios and proportions to show figures are similar or solve problems with similar figures.
PRACTICE: Review Worksheet; Pg 504 – 507 has even MORE practice if you want it.
Dilations as Proportions Notes
Ex) Rectangle CUTE was dilated to create rectangle UGLY. Find the length of LY.
C 8 cm
3 cm
E
U
T
U
7.5 cm
Y
G
L
Ex) Determine which of the following figures could be a dilation of the triangle to the right.
(There could be more than one answer)
A
16 in.
C
B
20 in.
D
8 in.
6 in.
30 in.
2.25 in.
6 in.
3 in.
10 in.
5 in.
1. Find the length of AB after the dilation.
A′
A
4m
6m
C
10 m
B
C′
B′
2. Which of the following could NOT be an enlargement or
reduction (dilation) of the original painting shown at right?
8 in
12 in
A
4 in
B
10 in
6 in
15 in
C
D
12 in
9in
13 in
18 in
Ratio Problems
Write the equation for each and solve. Show all work.
1. One angle of a triangle measures 18º. The other two angles are in the ratio of 4:5. Find the measures
of the angles.
2. The vertex angle and the one base angle of an isosceles triangle are in the ratio of 7:4. Find the
measures of the 3 angles.
3. The sides of a triangle have the ratio of 7:9:12. The perimeter of the triangle is 420. Find the length
of each side.
4. Two consecutive angles of a parallelogram are in a ratio of 7:3. Find the measures of the angles.
5. The angles of a pentagon are in a ratio of 7:6:5:5:4. Find the measures of each angle.
6. One angle of a hexagon is 120º. The other angles are in the ratio of 11:9:8:7:5. Find the measures of
the angles.
7. The sides of a quadrilateral are 5, 7, 4, and 8 cm. If the shortest side of a similar quadrilateral is
10cm, what is the length of the longest side?
8. If a rectangular I.D. card is 4cm x 8cm (l x w) is enlarged so that its new perimeter is 50cm, what is
the new width?
9. The base of an isosceles triangle is 12cm long and one of the legs is 6cm long. What is the
perimeter of a similar triangle whose base is 18cm?
10. The sides of a polygon are 3, 4, 7, 9, and 11 mm long. Find the perimeter of a similar polygon
whose shortest side is 10.5 mm long.
Notes: Similar Triangles
There are 3 ways you can prove triangles similar WITHOUT having to use all sides and angles.
Angle- Angle Similarity (AA~) – If two angle of one triangle are ______________ to two corresponding
angles of another triangle, then the triangles are similar
Side- Side- Side Similarity (SSS~) – If the three sides of one triangle are __________________ to the
three corresponding sides of another triangle, then the triangles are similar.
Side-Angle- Side Similarity (SAS~) – If two sides of one triangle are ____________________ to two
corresponding sides of another triangle and their included angles are ________________, then the triangles
are similar.
Examples: Determine if the triangles are similar. If so, tell why and write the similarity statement
and similarity ratio.
Similar : Y or N
Why:_________
Similar : Y or N
Why:_________
Similarity Statement :_______~__________
Similarity Statement :_______~__________
Similarity Ratio :__________
Similarity Ratio :__________
Similar : Y or N
Similar : Y or N
Why:_________
Why:_________
Similarity Statement :_______~__________
Similarity Statement :_______~__________
Similarity Ratio :__________
Similarity Ratio :__________
Notes: Properties of Similar Triangles
Ex. 1
Ex. 2
D
I
V
Y
ID DE

IV
E
O ID  DE
DV
A
E
L
R
P
S
AY YE

LA
AY AE

YR
LY

PL RS
PA AY

ES
Now that you can write the proportions, you can solve problems.
D
Ex. 3
Ex. 5
Ex. 4
5
I
x
x
Ex. 6 Find RV
V
x
Ex. 7 Find y
E
8
20
O
Proportional Relationships
Solve for the variable in each figure.
1. y =__________
10
x = __________
2. k =______________
5y – 2
5
12
3x + 2
2
3
9
2
k
4
3
x
3. SQ = x ; ST = 22 ;
SP = 12 ; PR = 4x+8
4. y =__________
x = __________
x
8
x = __________
16
5
y
3
20
Given: j k l
A
j
D
B
k
E
C
F
5. AC = 9; BC = 6; DF = 15
EF = __________
6. AB = 5y; DE = 2y; EF = 12
BC = ___________
l
7. BC = x + 2; BA = 9; EF = x + 3; ED = 12
x = _______; BC = ________; EF = _______
8. AC = 3x; BC = 16; EF = 20; FD = 4x -2
x = ______; AC = _______; FD = _______
Dilations & Similarity in the Coordinate Plane Notes
5.
7.
6.
8.
9.
10.
11. Given: E(–2, –6), F(–3, –2), G(2, –2), H(–4, 2), and J(6, 2).
Prove: ∆EHJ ~ ∆EFG.
12. Given: R(–2, 0), S(–3, 1), T(0, 1), U(–5, 3), and V(4, 3).
Prove: ∆RST ~ ∆RUV
Notes: Geometric Mean
The geometric mean of two positive numbers is the positive square root of their products. For
a x
 , the x
x b
is the geometric mean.
Examples: Find the geometric mean of the given numbers.
a. 4 and 9
b. 6 and 15
c. 2 and 8
The altitude to the hypotenuse of a right triangle forms two triangles that are ________________ to each
other and to the original triangle. In other words, there are ________ similar triangles: a small one, a
medium one, and a large one.
Examples:
Ex 1: m = 2, n = 10, h = _____
a
b
h
m
n
c
c
h
a
b
a
m
b
n
h
Ex 2: m = 2, n = 10, b = _____
a
You draw the similar triangles:
b
h
m
n
c
Geometric Mean
If ∆ABC is a right triangle and CD is the altitude to the hypotenuse AB then
C
m a
 →a² = mc
∆ABC ~ ∆CBD →
a c
n b
∆ABC ~ ∆ACD →  → b² = nc
a
b c
h
m h
∆ACD ~ ∆CBD →  → h² = mn
h n
A
m D
n
B
c
c
a
b
h
b
a
m
b
n
h
1. c = 12; m = 6; a = ?
2. m = 4; h = 25; n = ?
3. c = 12; m = 4; h = ?
4. a = 30; c = 50; h = ?
5. h = 12; m = 9; b = ?
6. a = 24; m = 4; b = ?
7. b = 45; n = 5; a = ?
8. b = 8; m = 12; c =?
10. a = 7 5 ; h = 14; c = ?; n = ?
11. a = 6 5 ; b = 3 5 ; m = ?; h = ?