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5-7 Similar Figures and Proportions Warm Up Problem of the Day Presentation Six Lessons Course 2 The relationship between scale factor, side lengths, perimeter ... – PowerPoint PPT presentation

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Title: Warm Up


1
Warm Up
Problem of the Day
Presentation Six Lessons
2
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
3
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
4
Lesson 1 EQ How can I determine if two figures
are similar?
5
Insert Lesson Title Here
Vocabulary Words
similar corresponding sides corresponding angles
6
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.
7
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.
8
Vocabulary
Matching sides of two or more polygons are called
corresponding sides, and matching angles are
called corresponding angles.
9
Symbols
?ABC
AB

and



10
(No Transcript)
11
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.
12
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.
13
Lesson 2 EQ How can I determine if figures are
similar based on their angle measure?
14
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
15
Insert Lesson Title Here
Try One
Tell whether the figures are similar. (Notice the
shapes are turned) 1.
similar
16
Insert Lesson Title Here
Try another
Tell whether the figures are similar. 2.
not similar
17
Lesson 3 EQ How can I determine the scale
factor of similar figures?
18
Vocabulary
Scale Factor The ratio of the lengths of
corresponding sides in similar figures
19
How can I determine the scale factor of similar
figures?
EXAMPLE 1 The figures below are similar
3
4
20
How can I determine the scale factor of similar
figures?
EXAMPLE 2 A B
2.5
A
5
B
2
1
21
Lesson 4 EQ What is the relationship between
the scale factor, side lengths, perimeter, and
area?
22
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
23
Lesson 5 EQ How can I determine missing side
lengths of similar figures?
24
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.
25
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.
26
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.
27
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.
28
Insert Lesson Title Here
Ticket-out-the-door
Find the unknown length in each pair of similar
figures.
1.
2.
29
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.
30
Lesson 6 EQ How can I use shadow math to find
missing side lengths?
31
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
32
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.
33
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.
34
Classwork
  • Problem 5.1(pg.78-79)
  • Problem 5.2 (pg. 80-81)
  • Problem 5.3 (pg. 82-83)
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