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

2. 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

3. 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

4.
Practice dialations and scale factors

5. 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.

6. 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.”

7. 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)

8. 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

9. 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

10. -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

11. 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.

12. 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

13. 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, even 3