Warm Up

1
Preview
Warm Up
California Standards
Lesson Presentation
2
Warm Up Solve each proportion.
1.
2.
b 10
y 8
m 52
3.
4.
p 3
3
(No Transcript)
4
Vocabulary
similar corresponding sides corresponding angles
5
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.
6
(No Transcript)
7
(No Transcript)
8
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.
9
Additional Example 1 Continued
Compare the ratios of corresponding sides to see
if they are equal.
20 20
The ratios are equal. Rectangle J is similar to
rectangle K. The notation J K shows similarity.
50 ? 48
The ratios are not equal. Rectangle J is not
similar to rectangle L. Therefore, rectangle K is
not similar to rectangle L.
10
Check It Out! Example 1
Which rectangles are similar?
8 ft
A
B
6 ft
C
5 ft
4 ft
3 ft
2 ft
Since the three figures are all rectangles, all
the angles are right angles. So the corresponding
angles are congruent.
11
Check It Out! Example 1 Continued
Compare the ratios of corresponding sides to see
if they are equal.
24 24
The ratios are equal. Rectangle A is similar to
rectangle B. The notation A B shows similarity.
16 ? 20
The ratios are not equal. Rectangle A is not
similar to rectangle C. Therefore, rectangle B is
not similar to rectangle C.
12
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.
14 1.5 w 10
Find the cross products.
21 10w
Divide both sides by 10.
2.1 w
The picture on the Web page should be 2.1 in.
wide.
13
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.
56 10 w 40
Find the cross products.
560 40w
Divide both sides by 40.
14 w
The painting displayed on the poster should be 14
in. long.
14
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?
Set up a proportion.
Find the cross products.
4.5 x 3 6
Multiply.
4.5x 18
15
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?
Solve for x.
The third side of the triangle is 4 ft long.
16
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?
Set up a proportion.
18 ft x in. 24 ft 4 in.
Find the cross products.
Multiply.
18x 96
17
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?
Solve for x.
The third side of the triangle is about 5.3 in.
long.
18
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.