Embed Size (px)
Citation preview
8-5 Indirect Measurement
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpFind the missing value in each proportion.
1. =
2. =
3. =
4. =
t = 15
k = 5
n = 56
Course 1
8-5 Indirect Measurement
6 t
__ 18 45
__
k19
__ 20 76
__
6 8
__ 42 n
__
2111
__ x 44
__ x = 84
Problem of the Day
Bryce, Kate, and Annie have drawn rectangles. Each side of Bryce’s rectangle is twice the size of one side of Kate’s. The same side of Kate’s rectangle is congruent to one side of Annie’s. One side of Annie’s rectangle is congruent to one side of Bryce’s. Which two rectangles could be congruent?
Kate’s and Annie’s
Course 1
8-5 Indirect Measurement
Learn to use proportions and similar figures to find unknown measures.
Course 1
8-5 Indirect Measurement
Vocabulary
indirect measurement
Insert Lesson Title Here
Course 1
8-5 Indirect Measurement
Course 1
8-5 Indirect Measurement
One way to find a height that you cannot measure directly is to use similar figures and proportions. This method is called indirect measurement.
Course 1
8-5 Indirect Measurement
Additional Example 1: Using Indirect Measurement
Use the similar triangles to find the height of the tree.
2 7
__ 6 h
__ =
h • 2 = 6 • 7
2h = 42
2h 2
___ 42 2
___ =
h = 21
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.
The tree is 21 feet tall.
Course 1
8-5 Indirect Measurement
Try This: Example 1
Use the similar triangles to find the height of the tree.
3 9
__ 6 h
__ =
h • 3 = 6 • 9
3h = 54
3h 3
___ 54 3
___ =
h = 18
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 3.
Divide both sides by 3 to undo multiplication.
The tree is 18 feet tall.
3 ft. 9 ft.
6 ft. h
Course 1
8-5 Indirect Measurement
Additional Example 2: Measurement Application
A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket?
91.5 3
____ h 4
__ =
4 • 91.5 = h • 3
366 = 3h
366 3
___ 3h 3
___ =
122 = h
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 3.
Divide both sides by 3 to undo multiplication.
The rocket is 122 feet tall.
Course 1
8-5 Indirect Measurement
Try This: Example 2
A building casts a shadow that is 72.5 feet long when a 4-foot model building casts a shadow that is 2 feet long. How tall is the building?
72.5 2
____ h 4
__ =
4 • 72.5 = h • 2
290 = 2h
290 2
___ 2h 2
___ =
145 = h
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.
The building is 145 feet tall.
h
72.5 ft 2 ft
4 ft
Lesson Quiz
1. On a sunny day, a telephone pole casts a
shadow 21 ft long. A 5-foot-tall mailbox next to
the pole casts a shadow 3 ft long. How tall is
the pole?
2. On a sunny afternoon, a goalpost casts a 75 ft
shadow. A 6.5 ft football player next to the
goal post has a shadow 19.5 ft long. How tall is
the goalpost?
25 feet
35 feet
Insert Lesson Title Here
Course 1
8-5 Indirect Measurement
