Pre-Algebra 7-6 Similar Figures 7-6 Similar Figures Pre-Algebra Warm Up Warm Up Problem of the Day...
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Transcript of Pre-Algebra 7-6 Similar Figures 7-6 Similar Figures Pre-Algebra Warm Up Warm Up Problem of the Day...
Pre-Algebra
7-6 Similar Figures7-6 Similar Figures
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
7-6 Similar Figures
Warm UpSolve each proportion.
Pre-Algebra
7-6 Similar Figures
b30
39
=1. 5635
y5
=2.
412
p9
=3. 56m
2826
=4.
b = 10 y = 8
p = 3 m = 52
Pre-Algebra
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
223
Pre-Algebra
7-6 Similar Figures
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. The 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.
0.15 0.151.510
=
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.0.25 0.2510
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.
6 in.x ft
4.5 in.3 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
4.5x = 3 • 6
4.5x = 18
x = = 4184.5
Cancel the units.
Multiply
Solve for x.
Additional Example 2 Continued
The third side of the triangle is 4 ft long.
Pre-Algebra
7-6 Similar Figures
Try This: Example 2
Set up a proportion.
24 ftx in.
18 ft4 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
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?
Pre-Algebra
7-6 Similar Figures
18x = 24 • 4
18x = 96
x = 5.39618
Cancel the units.
Multiply
Solve for x.
Try This: Example 2 Continued
The third side of the triangle is about 5.3 in. long.
Pre-Algebra
7-6 Similar Figures
The following are matching, or corresponding:A and X
Remember!
AB and XY
BC and YZ
AC and XZ
A
C BZ Y
X
C and Z
B and Y
Pre-Algebra
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
50 48
The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity.
The ratios are not equal. Rectangle J is not similar to rectangle L.
20 = 20
length of rectangle Jlength of rectangle K
width of rectangle Jwidth of rectangle K
10 5
42
? =
length of rectangle Jlength of rectangle L
width of rectangle Jwidth of rectangle L
1012
45
?=
Compare the ratios of corresponding sides to see if they are equal.
Pre-Algebra
7-6 Similar Figures
Try This: Example 3
Which rectangles are similar?
A8 ft
4 ft
B6 ft
3 ft
C5 ft
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
16 20
The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity.
The ratios are not equal. Rectangle A is not similar to rectangle C.
24 = 24
length of rectangle Alength of rectangle B
width of rectangle Awidth of rectangle B
8 6
43
? =
length of rectangle Alength of rectangle C
width of rectangle Awidth of rectangle C
8 5
42
?=
Compare the ratios of corresponding sides to see if they are equal.
Pre-Algebra
7-6 Similar Figures
Lesson QuizUse 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.
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. Which rectangles are similar?