Course 1 Warm Up Lesson Presentation Problem of the Day Warm Up Fill in the missing value 1 c 2 qt 2 180 in yd 3 3 tons lb 4 min 2760 s 8 5 6000 ID: 142822
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Slide1
7-4
Similar Figures
Course 1
Warm Up
Lesson Presentation
Problem of the DaySlide2
Warm Up
Fill in the missing value.
1.
c = 2 qt2. 180 in. = yd
3. 3 tons = lb4. min = 2,760 s
8
5
6,000
46Slide3
Problem of the Day
How many 8 in. by 10 in. rectangular tiles would be needed to cover a 16 ft by 20 ft floor?
576Slide4
Learn
to use proportions to find missing measures in similar figures.Slide5
Vocabulary
corresponding sides
corresponding angles
similarSlide6
Matching sides of two or more polygons are called
corresponding sides,
and matching angles are called corresponding angles.Slide7
Similar Figures
Two figures are similar if
• the measures of the corresponding angles are equal
• the ratios of the lengths of the corresponding sides
t
are proportional
Similar
figures have the same shape but not necessarily the same size.Slide8
Additional Example 1: Finding Missing Measures in Similar Figures
111
y
___
100
200
____
=
Write a proportion using corresponding side lengths.
The cross products are equal.
200 •
111
= 100
•
y
The two triangles are similar. Find the missing length
y
and the measure of
D
.Slide9
Additional Example 1 Continued
y is multiplied by 100.
22,200
= 100y
22,200
100
______
100
y
100
____
=
Divide both sides by 100 to undo the multiplication.
222 mm
=
y
Angle
D
is congruent to angle
C,
and
m C
= 70°.
m
D
= 70°
The two triangles are similar. Find the missing length
y
and the measure of
D
.Slide10
Check It Out: Example 1
52
y
___
50
100
____
=
Write a proportion using corresponding side lengths.
The cross products are equal.
100 •
52
= 50
•
y
A
B
60 m
120 m
50 m
100 m
y
52 m
65
°
45
°
The two triangles are similar. Find the missing length
y
and the measure of
B
.Slide11
Check It Out: Example 1 Continued
y is multiplied by 50.
5,200
= 50y
5,200
50
_____
50
y
50
___
=
Divide both sides by 50 to undo the multiplication.
104 m
=
y
Angle
B
is congruent to angle
A,
and
m A
= 65°.
m
B
= 65°
The two triangles are similar. Find the missing length
y
and the measure of
B
.Slide12
This reduction is similar to a picture that Katie painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting?
1
Understand the Problem
The
answer
will be the width of the actual painting.List the important information
:
The actual painting and the reduction above are
t
similar.
The reduced painting is 2 cm tall and 3 cm wide.
The actual painting is 54 cm tall.
Additional Example 2:
Problem Solving ApplicationSlide13
Additional Example 2 Continued
Draw a diagram to represent the situation. Use the corresponding sides to write a proportion.
2
Make a Plan
Reduced
Actual
2
54
3
wSlide14
Additional Example 2 Continued
Solve
3
54 •
3
= 2 • w
162
= 2
w
162
2
____
2
w
2
___
=
81
=
w
The width of the actual painting is 81 cm.
Write a proportion.
The cross products are equal.
w is multiplied by 2.
Divide both sides by 2 to undo the multiplication.
3 cm
w
cm
2 cm
54 cm
_____
=Slide15
Additional Example 2 Continued
Look Back
4
Estimate to check your answer. The ratio of the heights is about 2:50 or 1:25. The ratio of the widths is about 3:90, or 1:30. Since these ratios are close to each other, 81 cm is a reasonable answer.Slide16
Check It Out: Example 2
This reduction is similar to a picture that Marty designed. The height of the actual picture is 39 inches. What is the width of the actual picture?
1
Understand the Problem
The
answer
will be the width of the actual painting.
List the
important information
:
The actual painting and the reduction above are
t
similar.
The reduced painting is 3 in. tall and 4 in. wide.
The actual painting is 39 in. tall.
4 in.
3 in.Slide17
Check It Out: Example 2 Continued
Draw a diagram to represent the situation. Use the corresponding sides to write a proportion.
2
Make a Plan
Reduced
Actual
3
39
4
wSlide18
Check It Out: Example 2 Continued
Solve
3
4 in
w
in
____
3 in
39 in
_____
=
39 •
4
= 3
•
w
156
= 3
w
156
3
____
3
w
3
___
=
52
=
w
The width of the actual painting is 52 inches.
Write a proportion.
The cross products are equal.
w is multiplied by 3.
Divide both sides by 3 to undo the multiplication.Slide19
Check It Out: Example 2 Continued
Look Back
4
Estimate to check your answer. The ratio of the heights is about 4:40, or 1:10. The ratio of the widths is about 5:50, or 1:10. Since these ratios are the same, 52 inches is a reasonable answer.Slide20
Lesson Quiz
These two triangles are similar.
1.
Find the missing length x.
2. Find the measure of J.
3. Find the missing length y.4.
Find the measure of P.5. Susan is making a wood deck from plans for an 8 ft by 10 ft deck. However, she is going to increase its size proportionally. If the length is to be 15 ft, what will the width be?
36.9°
30 in.
4 in.
90°
12 ft