Transcript picture 18

Week 17, Day Two
HW # 59 - Yogurt MARS task AND complete any unfinished
CW work
Warm up
Solve each proportion.
1. 3 = b
9
3.
30
p = 4
9
12
b = 10
y = 56
2. 5
35
p=3
4.
28 = 56
26
m
y=8
m = 52
Warm Up Response
24
Homework Check
Ready to Go On p. 242 # 1-20 all
1) 19/8
11) about $4/lb
2) 3/2
12) minutes; 45 minutes
3) 1/1
13) $0.23/ egg; $ 0.25/ egg;
4) Yes
a dozen eggs
5) no
14) $300
6) yes
15) 240 miles
7) no
16) 99 minutes
8) no; he should have
17) 2.5 gal
used 2.25 cups
18) 1/5 km/s
9) 5.2 g/cm cubed
19) 4,400 ft/min
10) ~ 40 words/min
20) 4 yards/s (~ 8.2 mi/hr)
• Quick Pop Quiz on Chapter 5, sections 1-4
Worksheets (on your own when you are done)
• Problem Solving 5-5
• Challenge 5-5
As a class
• Proportion problems (if time)
Vocabulary
similar
corresponding sides
corresponding angles
Similar 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.
43°
43°
Reading Math
A is read as “angle A.” ∆ABC is read as “triangle ABC.”
“∆ABC ~∆EFG” is read as “triangle ABC is similar to triangle
EFG.”
Additional 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.
Additional Example 1 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
width of rectangle J
=
12
5
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.
Check It Out! Example 1
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.
Check It Out! Example 1 Continued
Compare the ratios of corresponding sides to see if they are equal.
length of rectangle A
length of rectangle B
8 ? 4
width of rectangle A
=
6
3
width of rectangle B
24 = 24
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
width of rectangle A
=
5
2
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.
Additional Example 2: Finding Missing Measures in
Similar Figures
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?
Set up a proportion. Let w be the width of the picture on the Web page.
width of a picture
width on Web page
14 ∙ 1.5 = w ∙ 10
21 = 10w
21
10w
=
10
10
14
w
=
10 height of picture
1.5 height on Web page
Find the cross products.
Divide both sides by 10.
2.1 = w
The picture on the Web page should be 2.1 in. wide.
Check It Out! Example 2
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?
Set up a proportion. Let w be the width of the painting on the Poster.
width of a painting
width of poster
56 ∙ 10 = w ∙ 40
56
w
=
40 length of painting
10 length of poster
Find the cross products.
560 = 40w
560
=
40
40w
40
Divide both sides by 40.
14 = w
The painting displayed on the poster should be 14 in. long.
Additional 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?
side of small triangle base of=
small triangle
4.5 in. = 3 ft
6 in.
x ft
4.5 • x = 3 • 6
4.5x = 18
side of large triangle base of
large triangle
Set up a proportion.
Find the cross products.
Multiply.
Additional Example 3 Continued
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?
x=
18
=4
4.5
Solve for x.
The third side of the triangle is 4 ft long.
Check It Out! Example 3
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
18 ft = 24 ft
4 in.
x in.
18 ft • x in. = 24 ft • 4 in.
18x = 96
base of large triangle base of
small triangle
Set up a proportion.
Find the cross products.
Multiply.
Check It Out! Example 3 Continued
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?
x=
96
 5.3
18
Solve for x.
The third side of the triangle is about 5.3 in. long.
Lesson 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.