Uses of SimilarityUses of Similarity

Indirect MeasurementScale Drawings and Models

Irma Crespo 2010

REVIEWREVIEW

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

4

4

2

2This ratio is

the scale factor.

Indirect MeasurementIndirect Measurement

With the properties of similarity, indirect measurement is possible.

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

Find LengthFind LengthCITY 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

_hydrant_street light

_5_26

= 2.5h

5h = 2.5 * 265h = 655h = 65 5 5 h = 13 feet

Your Turn (OHP)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?

Ponder ThisPonder 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?

ABAC

Find the DistanceFind the DistanceLAKES In the figure below, triangle DBA is similar to

triangle ECA. Ramon wants to know the distance across the lake.

C

A

B

DE

d m

162 m

40 m

320 m

= BDCE

320482

40d=

19,280 = 320 d

60.25 m = d

Your Turn (OHP)Your Turn (OHP)WALKING Find the distance from the park to the house.

T

Z

W

8m 4m5m

d m

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 ScaleFind 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?

modelactual

15 inches20 feet =

___1___x feet

LENGTH SCALE

15 x = 20 (1)

15 x = 20 15 15

x = 1 (1/3)

Your Turn (OHP)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?

SummarySummaryFor indirect measurement• find out the two things you are comparing• write the proportion • cross multiply and solve for the missing measurementFor scale drawings and models• scale = model measurement actual measurement • the proportion should show the ratio on lengths equals the

scale ratio

Exit SlipExit 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 WorksheetsPractice WorksheetsComplete the practice worksheet.

Work with a partner or on your own.

Submit completed worksheet for grading.

Solutions are discussed the next day.

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

Main ResourcesMain 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.