Ch. 4-5 Similarity Transformations Ch. 4-6 Scale Models and Maps Ch. 4-7 Similarity and Indirect Measurement

a transformation in which a figure and its image are similar dilation a transformation in which a figure and its image are similar Draw a dilation http://www.mathwarehouse.com/transformations/dilations/dilations-in-math.php

scale factor The ratio of a length in the image to the corresponding length in the original figure Scale factor of 1/2 Means the image will be half as big as the original Scale factor of 2 Means the image will be twice as big as the original Scale factor of 1 Means the image will be same size of the original

http://www.studyzone.org/mtestprep/math8/g/PracDil.htm Practice dialations and scale factors

Ch. 4-5 Similarity Transformations Example: The figure below has been dilated with center A by a scale factor of 1/2 C 20 10 10 5 A B 8 16 -To figure out the new side lengths, multiply each side by 1/2 or divide by two. In general you will always do this with the scale factor.

Example 1: Find the image of the triangle below after a dilation with center C and a scale factor of 1/3. C 6 6 D 18 9 18 E F B A 27 Example 2: Find the image of a triangle with vertices D(-2, 2), E(1, -1) and F(-2, -1) after a dilation with center D and a scale factor of 2. Need to multiply all of the coordinates by the scale factor of 2. The new coordinates are as follows DI(-4, 4), EI(2, -2), FI(-4, -2) You read DI as “D prime.”

Example 3: Find the coordinates of the image of quadrilateral KLMN after a dilation with a scale factor of 3/2. K(-4, 1) L(-2, 1) M(1, 1) N(1, -1) To find the new coordinates, multiply them by the scale factor 3/2. K(-4, 1) K I(-6, 3/2) L(-2, 1) LI(-3, 3/2) M(1, 1) MI(3/2, 3/2) N(1, -1) NI(3/2, -3/2) You try one: Find the coordinates of the image ABCD with vertices A(0, 0), B(0, 3), C(3, 3), and D(3, 0) after a dilation with a scale factor of 4/3. AI(0, 0) BI(0, 4) CI(4, 4) DI(4, 0)

This is an enlargement with scale factor 2 -an enlargement is a dilation with a scale factor greater than 1. -a reduction is a dilation with a scale factor less than 1. Example 4: Find the scale factor below and classify each as an enlargement or a reduction. 10 C B 12 14 This is a reduction with scale factor 1/2 5 BI CI 6 7 15 BI CI AI A 7.5 B C 24 This is an enlargement with scale factor 2 12 AI A D DI

Ch. 4-6 Scale Models and Maps and Ch Ch. 4-6 Scale Models and Maps and Ch. 4-7 Similarity and Indirect Measurement -a scale model is a model similar to the actual object it represents. -the scale of a models is the ratio of the length of the model to the corresponding length of the actual object. Example 1: Use proportions to solve the following problems. a.) The scale of a map is 1 in. : 10 mi. How many actual miles does 4.4 in. represent? b.) The scale of a map is 1 in. : 4 mi. How many inches does 86 miles represent? x = 44 miles x = 21.5 inches

-indirect measurement uses proportions and similar triangles to measure distances that would be difficult to measure directly. Example 2: A student is 5 ft. tall and casts a 15 ft. shadow. A nearby tree casts a shadow 75 ft. long. Find the height of the tree. 15x = 375 x = 25 ft. tall Example 3: A school 40 ft. high casts a 160 ft. shadow. A nearby cellular phone tower casts a 210 ft. shadow. Find the height of the tower. 160x = 8400 x = 52.5 ft. tall

Example 4: Use the similar triangles below to set up a proportion and solve for the unknown measurement. 15 ft. x x (16 * 15) / 30 = x x = 8 ft. 14 ft. 16 ft. 15 ft. Big x Small 30 ft. 16 ft.

Example 4: Use the similar triangles below to set up a proportion and solve for the unknown measurement. 5 ft. 6 ft. 3 ft. x (3 * 5) / 6 = x x = 2.5 ft. 5 ft. x. 6 ft. Big 3 ft. Small

Pg 189 #2-10 even 5 Pg 193 #4-10 even 4 Pg 198 #8-12 even 3 Homework d1 Pg 189 #2-10 even 5 Pg 193 #4-10 even 4 Pg 198 #8-12 even 3 Homework d2 Pg 189 #12-14 even 2 Pg 193 #12-16 even 3 Pg 198 #14, 18-20 even 3