Transcript 7-6

Ch. 7 Learning Goal: Ratios & Proportions
• Learn to find equivalent ratios to create proportions (7-1)
• Learn to work with rates and ratios (7-2)
• Learn to use one or more conversion factors to solve rate
problems (7-3)
• Learn to solve proportions (7-4)
• Learn to identify and create dilations of plane figures (7-5)
• Learn to determine whether figures are similar, to use scale
factors, and to find missing dimensions similar figures (7-6)
• Learn to make comparisons between and find dimensions of
scale drawings and actual objects (7-7)
• Learn to make comparisons between and find dimensions of
scale models and actual objects (7-8)
• Learn to make scale models of solid figures (7-9)
Page 364 #7-12 & #20-24 (SR)
7-6 Similar Figures
Pre-Algebra Homework
Page 370-371
#1-6 & #21-26
(Spiral Review)
Pre-Algebra
7-6
7-6 Similar
SimilarFigures
Figures
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
7-6 Similar Figures
Today’s Learning Goal Assignment
Learn to determine
whether figures are
similar, to use scale
factors, and to find
missing dimensions in
similar figures.
Pre-Algebra
7-6 Similar Figures
Vocabulary
similar
Pre-Algebra
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.
Pre-Algebra
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. They have the same shape, but they are
not the same size.
The ratio formed by the corresponding sides is the
scale factor.
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra