5-6
-
Upload
timon-espinoza -
Category
Documents
-
view
11 -
download
0
description
Transcript of 5-6
![Page 1: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/1.jpg)
5-6 Using Similar Figures
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
![Page 2: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/2.jpg)
Course 2
5-6 Using Similar Figures
Warm UpSolve each proportion.
1. k4
= 7525
2. 619
= 24x
3.
Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles.
J
N Z K O
A
JN KO
k = 12 x = 76
![Page 3: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/3.jpg)
Problem of the Day
Harvey starts to fill a 3-gallon tank from a hose that delivers 1 gallon per minute. However, the tanks leaks 1 quart per minute. In how many minutes will the tank begin to overflow?4
Course 2
5-6 Using Similar Figures
![Page 4: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/4.jpg)
Learn to use similar figures to find unknown lengths.
Course 2
5-6 Using Similar Figures
![Page 5: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/5.jpg)
Vocabulary
indirect measurement
Insert Lesson Title Here
Course 2
5-6 Using Similar Figures
![Page 6: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/6.jpg)
Course 2
5-6 Using Similar Figures
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.
![Page 7: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/7.jpg)
Find the unknown length in similar figures.
Additional Example 1: Finding Unknown Lengths in Similar Figures
ACQS
= ABQR Write a proportion using corresponding sides.
1248
= 14w
Substitute lengths of the sides.
12 · w = 48 · 14 Find the cross product.12w = 672 Multiply.
12w12
= 67212
w = 56
QR is 56 centimeters.
Divide each side by 12 to isolate the variable.
Course 2
5-6 Using Similar Figures
![Page 8: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/8.jpg)
Check It Out: Example 1
Insert Lesson Title Here
Course 2
5-6 Using Similar Figures
A B
C D
10 cm
12 cm
Q R
S T
24 cm
ACQS
= ABQR
Write a proportion using corresponding sides.
1224
= 10x
Substitute lengths of the sides.
12 · x = 24 · 10 Find the cross product.
12x = 240 Multiply.
12x12
= 24012
x = 20
QR is 20 centimeters.
Divide each side by 12 to isolate the variable.
Find the unknown length in similar figures.x
![Page 9: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/9.jpg)
The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.
Insert Lesson Title Here
Course 2
5-6 Using Similar Figures
Let x = the base of the inside triangle.
82
=12x
8 · x = 2 · 128x = 24
8x8
= 248
x = 3The base of the inside triangle is 3 inches.
Write a proportion using corresponding sidelengths.
Find the cross products.Multiply.
Divide each side by 8 to isolate the variable.
Additional Example 2: Measurement Application
![Page 10: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/10.jpg)
Check It Out: Example 2
The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.
Insert Lesson Title Here
Course 2
5-6 Using Similar Figures
3 cm
6 cm12 cm
Let w = the width of the right rectangle.
612
= 3w
6 ·w = 12 · 3
6w = 36
6w6
= 366
w = 6
The right rectangle is 6 cm wide.
Write a proportion using correspondingside lengths.
Find the cross products.Multiply.
Divide each side by 6 to isolate the variable.
?
![Page 11: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/11.jpg)
Additional Example 3: Estimating with Indirect Measurement
Course 2
5-6 Using Similar Figures
City officials want to know the height of a traffic light. Estimate the height of the traffic light.
27.2515
= 48.75h
Write a proportion.
Use compatible numbers to estimate.
53
≈ 50h
Simplify.
5h ≈ 150
The traffic light is about 30 feet tall.
27.25 ft
48.75 ft
h ft 2515
≈ 50h
Cross multiply.
h ≈ 30 Divide each side by 5 to isolate the variable.
![Page 12: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/12.jpg)
Check It Out: Example 3
Course 2
5-6 Using Similar Figures
The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle.
514.75
= h30.25
Write a proportion.
Use compatible numbers to estimate.
13
≈ h30
Simplify.
1 • 30 ≈ 3 • h
The outside triangle is about 10 feet tall.
14.75 ft
30.25 ft
h ft
515
≈ h30
30 ≈ 3h Divide each side by 3 to isolate the variable.
5 ft
Cross multiply.
10 ≈ h
![Page 13: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/13.jpg)
Lesson Quiz: Part I
Find the unknown length in each pair of similar figures.
Insert Lesson Title Here
Course 2
5-6 Using Similar Figures
1.
2.
x = 120 cm
t = 150 cm
![Page 14: 5-6](https://reader035.fdocuments.net/reader035/viewer/2022072016/56813324550346895d9a074b/html5/thumbnails/14.jpg)
Lesson Quiz: Part II
Find the unknown length in each pair of similar figures.
Insert Lesson Title Here
Course 2
5-6 Using Similar Figures
3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake.
about 15 inches