7-6 - auburnmath

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Transcript 7-6 - auburnmath

7-6 Similar Figures
Warm Up
Problem of the Day
Lesson Presentation
Course 3
7-6 Similar Figures
Warm Up
Solve each proportion.
1. 3 = b
9
30
3. p = 4
9
Course 3
12
b = 10
p=3
2.
y = 56
35
5
4. 28 = 56
26
m
y=8
m = 52
7-6 Similar Figures
Problem of the Day
A plane figure is dilated and gets 50%
larger. What scale factor should you use to
dilate the figure back to its original size?
(Hint: The answer is not 1 ).
2
2
3
Course 3
7-6 Similar Figures
Learn to determine whether figures are
similar, to use scale factors, and to find
missing dimensions in similar figures.
Course 3
7-6 Similar
Insert Lesson
FiguresTitle Here
Vocabulary
similar
Course 3
7-6 Similar Figures
The heights of letters in newspapers and on
billboards are measured using points and picas.
There are 12 points in 1 pica and 6 picas in one
inch.
A letter 36 inches tall on a billboard would be
216 picas, or 2592 points. The first letter in this
paragraph is 12 points.
Course 3
7-6 Similar Figures
Congruent figures have the same size and shape.
Similar figures have the same shape, but not
necessarily the same size. The A’s in the table are
similar. The have the same shape, but they are not
the same size.
The ratio formed by the corresponding sides is the
scale factor.
Course 3
7-6 Similar Figures
Additional Example 1: Using Scale Factors to Find
Missing Dimensions
A picture 10 in. tall and 14 in. wide is to be
scaled to 1.5 in. tall to be displayed on a Web
page. How wide should the picture be on the
Web page for the two pictures to be similar?
To find the scale factor, divide the known
measurement of the scaled picture by the
corresponding measurement of the original picture.
1.5 = 0.15
0.15
10
Then multiply the width of the original picture by
the scale factor.
2.1
14 • 0.15 = 2.1
The picture should be 2.1 in. wide.
Course 3
7-6 Similar Figures
Try This: Example 1
A painting 40 in. tall and 56 in. wide is to be
scaled to 10 in. tall to be displayed on a
poster. How wide should the painting be on
the poster for the two pictures to be similar?
To find the scale factor, divide the known
measurement of the scaled painting by the
corresponding measurement of the original
painting.
10 = 0.25
0.25
40
Then multiply the width of the original painting by
the scale factor.
14
56 • 0.25 = 14
The painting should be 14 in. wide.
Course 3
7-6 Similar Figures
Additional Example 2: Using Equivalent Ratios to
Find Missing Dimensions
A T-shirt design includes an isosceles triangle
with side lengths 4.5 in, 4.5 in., and 6 in. An
advertisement shows an enlarged version of the
triangle with two sides that are each 3 ft. long.
What is the length of the third side of the
triangle in the advertisement?
Set up a proportion.
4.5 in. = 6 in.
3 ft
x ft
4.5 in. • x ft = 3 ft • 6 in.
Find the cross products.
4.5 in. • x ft = 3 ft • 6 in.
in. • ft is on both sides
Course 3
7-6 Similar Figures
Additional Example 2 Continued
4.5x = 3 • 6
Cancel the units.
4.5x = 18
Multiply
x = 18 = 4
4.5
Solve for x.
The third side of the triangle is 4 ft long.
Course 3
7-6 Similar Figures
Try This: Example 2
A flag in the shape of an isosceles triangle with
side lengths 18 ft, 18 ft, and 24 ft is hanging on
a pole outside a campground. A camp t-shirt
shows a smaller version of the triangle with two
sides that are each 4 in. long. What is the length
of the third side of the triangle on the t-shirt?
Set up a proportion.
18 ft = 24 ft
4 in.
x in.
18 ft • x in. = 24 ft • 4 in. Find the cross products.
18 ft • x in. = 24 ft • 4 in. in • ft is on both sides
Course 3
7-6 Similar Figures
Try This: Example 2 Continued
18x = 24 • 4
Cancel the units.
18x = 96
Multiply
x = 96  5.3
18
Solve for x.
The third side of the triangle is about 5.3 in.
long.
Course 3
7-6 Similar Figures
Remember!
A
C
X
B
Z
Y
The following are matching, or corresponding:
A and X
AB and XY
B and Y
BC and YZ
C and Z
Course 3
AC and XZ
7-6 Similar Figures
Additional Example 3: Identifying Similar Figures
Which rectangles are similar?
Since the three figures are all rectangles, all the
angles are right angles. So the corresponding
angles are congruent.
Course 3
7-6 Similar Figures
Additional Example 3 Continued
Compare the ratios of corresponding sides to see if they are equal.
length of rectangle J
length of rectangle K
10 ? 4
5 =2
20 = 20
width of rectangle J
width of rectangle K
The ratios are equal. Rectangle J is similar to
rectangle K. The notation J ~ K shows similarity.
length of rectangle J
length of rectangle L
10 ? 4
12 = 5
width of rectangle J
width of rectangle L
50  48
The ratios are not equal. Rectangle J is not similar to
rectangle L. Therefore, rectangle K is not similar to
rectangle L.
Course 3
7-6 Similar Figures
Try This: Example 3
Which rectangles are similar?
8 ft
A
4 ft
6 ft
B
3 ft
5 ft
C
2 ft
Since the three figures are all rectangles, all the
angles are right angles. So the corresponding
angles are congruent.
Course 3
7-6 Similar Figures
Try This: Example 3
Compare the ratios of corresponding sides to see if they are equal.
length of rectangle A
length of rectangle B
8 ? 4
6 =3
24 = 24
width of rectangle A
width of rectangle B
The ratios are equal. Rectangle A is similar to
rectangle B. The notation A ~ B shows similarity.
length of rectangle A
length of rectangle C
8 ? 4
5= 2
width of rectangle A
width of rectangle C
16  20
The ratios are not equal. Rectangle A is not similar
to rectangle C. Therefore, rectangle B is not similar
to rectangle C.
Course 3
7-6 Similar Figures
Lesson Quiz
Use the properties of similar figures to
answer each question.
1. A rectangular house is 32 ft wide and 68 ft long.
On a blueprint, the width is 8 in. Find the length
on the blueprint. 17 in.
2. Karen enlarged a 3 in. wide by 5 in. tall photo into
a poster. If the poster is 2.25 ft wide, how tall is
it? 3.75 ft
3. Which rectangles are
similar?
A and B are similar.
Course 3