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 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.

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 _hydrant_ street light _5_ 26 = 2.5 h 5h = 2.5 * 26 5h = 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?

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?

AB AC Find the Distance  LAKES In the figure below, triangle DBA is similar to triangle ECA. Ramon wants to know the distance across the lake. C A B D E d m 162 m 40 m 320 m = BD CE d = 19,280 = 320 d m = d

Your Turn (OHP)  WALKING Find the distance from the park to the house. T Z W 8m4m 5m d m

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  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? model actual 15 inches 20 feet = ___1___ x feet LENGTHSCALE 15 x = 20 (1) 15 x = x = 1 (1/3)

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  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  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. 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 Resources Lesson Plan Problems (4-9;4-10)Math Connects: Concepts, Skills, and Problem Solving; Teacher Edition; Course 3, Volume 1 Columbus:McGraw-Hill, PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter 2010.