Warm Up

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Warm Up
Problem of the Day
Presentation Six Lessons
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Warm Up Find the cross products, then tell
whether the ratios are equal.
16 6
40 15
,
1.
240 240 equal
3 8
18 46
,
2.
8 9
24 27
,
3.
216 216 equal
28 12
42 18
,
4.
504 504 equal
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Problem of the Day Every 8th telephone pole along
a road has a red band painted on it. Every 14th
pole has an emergency call phone on it. What is
the number of the first pole with both a red band
and a call phone?
56
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Lesson 1 EQ How can I determine if two figures
are similar?
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Insert Lesson Title Here
Vocabulary Words
similar corresponding sides corresponding angles
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Similarity in the Real World
Octahedral fluorite is a crystal found in nature.
It grows in the shape of an octahedron, which is
a solid figure with eight triangular faces. The
triangles in different-sized fluorite crystals
are similar figures. Similar figures have the
same shape but not necessarily the same size.
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Vocabulary
SIMILAR FIGURES
Two figures are similar if The measures of their corresponding angles are equal. The ratios of the lengths of the corresponding sides are proportional.
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Vocabulary
Matching sides of two or more polygons are called
corresponding sides, and matching angles are
called corresponding angles.
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Symbols
?ABC
AB

and



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Example 1 Determining Whether Two Triangles Are
Similar
Identify the corresponding sides in the pair of
triangles. Then use ratios to determine whether
the triangles are similar.
E
16 in
10 in
A
C
28 in
D
4 in
7 in
40 in
F
B
AB DE
BC EF
AC DF
Step 1 Write ratios using the corresponding
sides.
4 16
7 28
10 40
Step 2 Substitute the length of the sides.
1 4
1 4
1 4
Step 3 Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the triangles are similar.
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Check It Out Example 2
Identify the corresponding sides in the pair of
triangles. Then use ratios to determine whether
the triangles are similar.
E
9 in
9 in
A
C
21 in
D
3 in
7 in
27 in
F
B
AB DE
BC EF
AC DF
Write ratios using the corresponding sides.
3 9
7 21
9 27
Substitute the length of the sides.
1 3
1 3
1 3
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the triangles are similar.
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Lesson 2 EQ How can I determine if figures are
similar based on their angle measure?
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How can I determine if these shapes are similar?
Tell whether the figures are similar.
Yes.The corresponding angles of the figures
have equal measure.
D
60
F
E
A
60
remember the sum of the interior angles of a
triangle 180
C
B
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Insert Lesson Title Here
Try One
Tell whether the figures are similar. (Notice the
shapes are turned) 1.
similar
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Insert Lesson Title Here
Try another
Tell whether the figures are similar. 2.
not similar
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Lesson 3 EQ How can I determine the scale
factor of similar figures?
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Vocabulary
Scale Factor The ratio of the lengths of
corresponding sides in similar figures
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How can I determine the scale factor of similar
figures?
EXAMPLE 1 The figures below are similar
3
4
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How can I determine the scale factor of similar
figures?
EXAMPLE 2 A B
2.5
A
5
B
2
1
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Lesson 4 EQ What is the relationship between
the scale factor, side lengths, perimeter, and
area?
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The relationship between scale factor, side
lengths, perimeter, and area...
5.5 ft
Figure A B Ratio/Scale Factor
Corresponding Sides
Side Lengths (feet)
Perimeter
Area
11 ft
3 ft
6 ft
5 ft
10 ft
The scale factor tells you the ratio of
corresponding side lengths and the ratio of the
perimeters The scale factor SQUARED tells you
the ratio of the areas
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Lesson 5 EQ How can I determine missing side
lengths of similar figures?
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Example 1 Missing Side Lengths
Find the unknown length in similar figures.
AC QS
AB QR

Step 1 Write a proportion using corresponding
sides.
12 48
14 w

Step 2 Substitute lengths of the sides.
12 w 48 14
Step 3 Cross multiply and divide.
12w 672
12w 12
672 12

Divide each side by 12 to isolate the variable.
w 56
QR is 56 centimeters.
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Insert Lesson Title Here
Check It Out Example 2
Find the unknown length in similar figures.
x
Q
R
10 cm
A
B
24 cm
12 cm
D
C
T
S
AC QS
AB QR

Write a proportion using corresponding sides.
12 24
10 x
Substitute lengths of the sides.

12 x 24 10
Find the cross product.
12x 240
Multiply.
12x 12
240 12
Divide each side by 12 to isolate the variable.

x 20
QR is 20 centimeters.
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Insert Lesson Title Here
Example 3 Measurement Application
The inside triangle is similar in shape to the
outside triangle. Find the length of the base of
the inside triangle.
Let x the base of the inside triangle.
8 2
12 x
Write a proportion using corresponding
side lengths.

8 x 2 12
Find the cross products.
8x 24
Multiply.
8x 8
24 8

Divide each side by 8 to isolate the variable.
x 3
The base of the inside triangle is 3 inches.
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Insert Lesson Title Here
Example 4
The rectangle on the left is similar in shape to
the rectangle on the right. Find the width of the
right rectangle.
12 cm
6 cm
3 cm
?
Let w the width of the right rectangle.
6 12
3 w
Write a proportion using corresponding side
lengths.

6 w 12 3
Find the cross products.
Multiply.
6w 36
36 6
6w 6

Divide each side by 6 to isolate the variable.
w 6
The right rectangle is 6 cm wide.
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Insert Lesson Title Here
Ticket-out-the-door
Find the unknown length in each pair of similar
figures.
1.
2.
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Insert Lesson Title Here
Ticket-out-the-door
Find the unknown length in each pair of similar
figures.
3. The width of the smaller rectangular cake is
5.75 in. The width of a larger rectangular cake
is 9.25 in. Estimate the length of the larger
rectangular cake.
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Lesson 6 EQ How can I use shadow math to find
missing side lengths?
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Example 1 Missing Side Lengths
Step 1 Label Corresponding Parts.
Step 2 Write a Proportion.
Step 3 Cross multiply and divide.
x
1.5m
5m
1m
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Additional Example 2 Estimating with Indirect
Measurement
City officials want to know the height of a
traffic light. Estimate the height of the traffic
light.
48.75 h
27.25 15

Step 1 Label Corresponding Parts.
27 15
49 h
h ft

9 5
49 h
Step 2 Write a Proportion

27.25 ft
9h 245
Step 3 Cross multiply.
48.75 ft
h 27
Multiply each side by 9 to isolate the variable.
The traffic light is about 30 feet tall.
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Check It Out Example 3
The inside triangle is similar in shape to the
outside triangle. These are called NESTED
triangles. Find the height of the outside
triangle.
h 30.25
5 14.75

Write a proportion.
Use compatible numbers to estimate.
5 15
h 30

h ft
5 ft
13
h 30

Simplify.
Cross multiply.
1 30 3 h
14.75 ft
Multiply each side by 5 to isolate the variable.
30 3h
30.25 ft
10 h
The outside triangle is about 10 feet tall.
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Classwork

• Problem 5.1(pg.78-79)
• Problem 5.2 (pg. 80-81)
• Problem 5.3 (pg. 82-83)