Warm up Week 17 Day Two Solve each proportion b 30 3 9 1 56 35 y 5 2 4 12 p 9 3 56 m 28 26 4 b 10 y 8 p 3 m 52 Warm Up Response 24 ID: 933334
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Slide1
HW # 59 - Yogurt MARS task AND complete any unfinished CW workWarm up
Week 17, Day Two
Solve
each proportion.
b
30
39
=
1.
56
35
y5
=
2.
4
12
p9
=
3.
56
m
2826
=
4.
b = 10
y = 8
p = 3
m = 52
Slide2Warm Up Response24
Slide3Homework Check
Ready to Go On p. 242 # 1-20 all1) 19/82) 3/23) 1/1
4) Yes5) no6) yes7) no8) no; he should have used 2.25 cups9) 5.2 g/cm cubed10) ~ 40 words/min
11) about $4/lb12) minutes; 45 minutes13) $0.23/ egg; $ 0.25/ egg; a dozen eggs14) $30015) 240 miles16) 99 minutes17) 2.5 gal18) 1/5 km/s19) 4,400
ft/min20) 4 yards/s
(~ 8.2 mi/hr)
Slide4Goals for Today
Quick
Pop Quiz on Chapter 5, sections 1-4Worksheets (on your own when you are done) Problem Solving 5-5Challenge 5-5 As a classProportion
problems (if time)
Slide5Vocabulary
similar
corresponding sides
corresponding angles
Slide6Similar
figures have the same shape, but not necessarily the same size.
Corresponding sides of two figures are in the same relative position, and corresponding angles are in the same relative position. Two figures are similar if the lengths of corresponding sides are proportional and the corresponding angles have equal measures.
Slide743°
43°
Slide8
A
is read as “angle A.” ∆ABC is read as “
triangle ABC.” “∆ABC ~∆EFG” is read as “triangle ABC
is similar to triangle EFG
.”
Reading Math
Slide9Additional Example 1: 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.
Slide10Additional Example 1 Continued
50
48The 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. Therefore, rectangle K 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
J
length of rectangle
L
width of rectangle J
width of rectangle L
10
12
45
?=
Compare the ratios of corresponding sides to see if they are equal.
Slide11Check It Out!
Example 1
Which rectangles are similar?
A
8 ft
4 ft
B
6 ft
3 ft
C
5 ft
2 ft
Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.
Slide12Check It Out!
Example 1 Continued
16
20The 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. Therefore, rectangle B 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
A
length 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.
Slide1314 ∙ 1.5
= w ∙ 10
Find the cross products.
Divide both sides by 10.
10
w10
2110
=
width of a picture
width on Web page
height of picture
height on Web page
14
w
=
101.5
2.1 = w
Set up a proportion. Let w be the width of the picture on the Web page.
The picture on the Web page should be 2.1 in. wide.
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?
Additional Example 2: Finding Missing Measures in Similar Figures
21
=
10
w
Slide1456 ∙ 10
= w ∙ 40
Find the cross products.
Divide both sides by 40.
40
w40
56040
=
width of a painting
width of poster
length of painting
length of poster
56
w
=
4010
14 = w
Set up a proportion. Let w be the width of the painting on the Poster.
The painting displayed on the poster should be 14 in. long.
Check It Out!
Example 2
560
=
40
w
A painting 40 in. long and 56 in. wide is to be scaled to 10 in. long to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar?
Slide15Additional Example 3:
Business Application
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.
3 ft
x
ft
4.5 in.6 in.
=
4.5 •
x = 3 • 6
Find the cross products.
side of small triangle base of small triangle
side of large triangle base of large triangle
=
4.5
x = 18
Multiply.
Slide16x
= = 4
18
4.5
Solve for x.
Additional Example 3 Continued
The third side of the triangle is 4 ft long.
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?
Slide17Check It Out!
Example 3
Set up a proportion.
24 ft
x
in.18 ft
4 in. =
18 ft •
x in. = 24 ft • 4 in.
Find the cross products.
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?
side of large triangle
side of small triangle
base of large triangle base of small triangle
=
18
x = 96
Multiply.
Slide18x
=
5.3
9618
Solve for x.
Check It Out!
Example 3 Continued
The third side of the triangle is about 5.3 in. long.
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?
Slide19Lesson Quiz
Use the properties of similar figures to answer each question.
1.
Which rectangles are similar?
A
and
B
are similar.
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.
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.