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Uses of Similarity. Indirect Measurement Scale Drawings and Models. Irma Crespo 2010. Similar figures have the same corresponding angles and the ratios of their corresponding side lengths are equal. 4. 2. 2. 4. REVIEW. This ratio is the scale factor.

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uses of similarity

Uses of Similarity

Indirect Measurement

Scale Drawings and Models

Irma Crespo 2010

review
Similar figures have the same corresponding angles and the ratios of their corresponding side lengths are equal.

4

2

2

4

REVIEW

This ratio is the scale factor.

indirect measurement
With the properties of similarity, indirect measurement is possible.

Indirect measurement is finding distances or lengths that are difficult to measure directly.

Indirect Measurement
find length
CITY PROPERTY

A fire hydrant 2.5 feet high casts a 5-foot shadow. How tall is a street light that casts a 26-foot shadow at the same time?

Let h represent the height of the street light.

h feet

26 feet

2.5 feet

5 feet

Find Length

_hydrant_

street light

_5_

26

2.5

h

=

5h = 2.5 * 26

5h = 65

5h = 65

5 5

h = 13 feet

your turn ohp
STREETS At the same time, a 2-meter street sign casts a 3-meter shadow, a telephone pole casts a 12.3 meter shadow. How tall is the telephone pole?Your Turn (OHP)
ponder this
In the problems presented, why are shadows measured at the same time?

What might happen to the measurements if the shadows are measured at different times?

Ponder This
find the distance
LAKES In the figure below, triangle DBA is similar to triangle ECA. Ramon wants to know the distance across the lake.

162 m

C

B

320 m

d m

40 m

A

E

D

Find the Distance

AB

BD

=

AC

CE

40

320

=

d

482

19,280 = 320 d

60.25 m = d

your turn ohp8

W

d m

8m

4m

Z

5m

T

Your Turn (OHP)
  • WALKING Find the distance from the park to the house.
scale drawings and models
Scale Drawings and Models
  • When representing an object that is either too large or too small to be drawn or to be built at actual size, scale drawings or models are needed.
  • scale = model measurement

actual measurement

find the scale
Find the Scale
  • MOVIES One of the models of a dinosaur used in the filming of a movie was only 15 inches tall. In the movie, the dinosaur appeared to have an actual height of 20 feet. What was the scale of the model?

LENGTH

SCALE

model

actual

15 inches

20 feet

___1___

x feet

=

15 x = 20 (1)

15 x = 20

15 15

x = 1 (1/3)

your turn ohp11
Your Turn (OHP)
  • ARCHITECTURE The model Mr. Vicario made of the building he designed is 25.6 centimeters? If the actual building is to be 64 meters tall, what is the scale of his model?
summary
Summary
  • For indirect measurement
  • find out the two things you are comparing
  • write the proportion
  • cross multiply and solve for the missing measurement
  • For scale drawings and models
  • scale = model measurement

actual measurement

  • the proportion should show the ratio on lengths equals the scale ratio
exit slip
Exit Slip
  • How do indirect measurement and scale models use the idea of similarity in polygons?
  • Submit this for a 2-point extra credit on a separate sheet of paper.
  • Don’t forget to write your name.
practice worksheets

Complete the practice worksheet.

Skills Practice: Lesson 4-9, Page 61 and 4-10, Page 67

Work with a partner or on your own.

Submit completed worksheet for grading.

Solutions are discussed the next day.

Practice Worksheets
main resources
Main Resources
  • Lesson Plan Problems (4-9;4-10)Math Connects: Concepts, Skills, and Problem Solving; Teacher Edition; Course 3, Volume 1
  • Columbus:McGraw-Hill, 2009.
  • PowerPoint created by Irma Crespo.

University of Michigan-Dearborn, School of Education. Winter 2010.