Transcript PPT 5-7 Similar Figures - PMS-Math

5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Warm Up
Solve each proportion.
1. 3 = b
9
b
=
10
30
2. y = 56
5
35
y=8
There are 24 students in Juan’s class. The ratio
3. of girls to boys is 1:2. How many girls and boys
8 girls and 16 boys
are in Juan’s class?
4.Three are 32 green and purple markers in a box. The ratio of
green markers to purple markers is 3:5. How many of the
markers are purple?
20
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Homework Review
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Daily Quiz
1. Tim can decorate 3 T-shirts in 20 minutes.
How many T-shirts can he decorate in 180
minutes? 27
2. A company produced blue T-shirts and red Tshirts in the ratio of 22:8. In one hour, the
company produced 120 red T-shirts. How
many blue T-shirts did the company produce
in that hour?
330
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Learn to determine whether figures are
similar and to find missing dimensions in
similar figures.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Corresponding sides & Corresponding angles
Sides or angles in the same position on each
triangle. Example:
p and b
r and c
q and a
A
Q and A
R and C
P and B
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
For two polygons to be similar:
1. Corresponding angles must have the same
measures.
2. The ratios of the lengths of the corresponding sides
must be proportional.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Example of similar figures.
Proportions the same.
Angles the same.
Size NOT the same.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
New Ferrari V4 Motorcycle Concept
designed by Amir Glink
Packed with a modified engine from a Ferrari Enzo!
The hand controls are from a F-16 fighter jet
Buttons are from a Forumla 1 race car
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Additional Example 1 Continued
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. Therefore, rectangle K is not similar to
rectangle L.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Try It: 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.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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
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. Therefore, rectangle B is not similar
to rectangle C.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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
10
=
w
1.5
height of picture
height on Web page
14 ∙ 1.5 = w ∙ 10
Find the cross products.
21 = 10w
21
10w
Divide both sides by 10.
=
10
10
2.1 = w
The picture on the Web page should be 2.1 in. wide.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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
40
width of a painting
length of painting
=
w
10
width of poster
length of poster
56 ∙ 10 = w ∙ 40
Find the cross products.
560 = 40w
560
40w
=
40
40
14 = w
Divide both sides by 40.
The painting displayed on the poster should be 14 in. long.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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?
4.5 in. = 6 in.
3 ft
x ft
Set up a proportion.
4.5 • x = 3 • 6
Find the cross products.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Additional Example 3 Continued
4.5x = 18
x = 18 = 4
4.5
Multiply.
Solve for x.
The third side of the triangle is 4 ft long.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
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?
18 ft = 24 ft
4 in.
x in.
Set up a proportion.
18 • x = 24 • 4
Find the cross products.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Check It Out: Example 3 Continued
18x = 96
x = 96  5.3
18
Multiply.
Solve for x.
The third side of the triangle is about 5.3 in. long.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in 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.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Lesson Quiz for Student Response Systems
1. A rectangular garden is 45 ft wide and 70 ft
long. On a blueprint, the width is 9 in. Identify the
length on the blueprint.
A. 7 in.
B. 9 in.
C. 12 in.
D. 14 in.
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Lesson Quiz for Student Response Systems
2. Rob enlarged a 4 in. wide by 7 in. tall picture
into a banner. If the banner is 3.5 ft wide, how tall
is it?
A. 6.05 ft
B. 6.125 ft
C. 7 ft
D. 7.125 ft
5-5
Students will be able to determine whether figures are similar
and find missing dimensions in similar figures.
Lesson Quiz for Student Response Systems
3. Which triangles are similar?
A. X and Y
Y
B. X and Z
C. Y and Z
D. none
X
Z