Uses of Similarity Indirect Measurement Scale Drawings and Models Irma Crespo 2010.
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Transcript of Uses of Similarity Indirect Measurement Scale Drawings and Models Irma Crespo 2010.
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.