1. 1. Have your homework out to be stamped. 2
1. Have your homework out to be stamped. 2. Complete the next 2 sections of your SKILL BUILDER.

2. x² + 21² = 25² x² + 441 = 625 x² = 184 x = 13.56 x = 13.6 MONDAY
Name: __________________________________________ Date: ______________________ Period: ____
Weekly Homework 8th Show all of your work to get credit.
MONDAY
The following pairs of angle measures are the measures of two angles of two triangles. Which pair of triangles would be similar because they have two pair of congruent angles?
A 48° and 50°; 92° and 50°
B 102° and 60°; 28° and 60°
C 48° and 30°; 92° and 48°
D 48° and 70°; 62° and 70°
2. The side view of a roof is shown below.
What is x, the height of the roof to the nearest tenth of a foot?
82˚
33˚
18˚
92˚
102˚
40˚
62˚
48˚
x² + 21² = 25²
x² = 625
x² = 184
x = 13.56
x = 13.6

3. 2 - d
6h + 4
-10c² - 15
8k² - 24k + 12
x -8
x -21
x -12

4. Transformations: Dilations

5. What is a Dilation?
Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure.
You are probably familiar with the term ‘dilate’ in reference to the eye doctor.
When doctors dilate your eyes, they are making the pupils larger for a better view of the back if the eye.

6. Proportionally
Let’s take a look…
And, of course, increasing the circle increases the diameter.
When a figure is dilated, it must be proportionally larger or smaller than the original.
So, we always have a circle with a certain diameter. We are just changing the size or scale.
Decreasing the size of the circle decreases the diameter.
We have a circle with a certain diameter.
Same shape, Different scale.

7. Which of these are dilations??
HINT: SAME SHAPE, DIFFERENT SIZE
Which of these are dilations?? C A B D
Discuss slides before clicking for the answer.
A is not a dilation because the milk containers are not the same shape.
B is a dilation because it is the same image, same size just a different scale or size.
C is a dilation because it is the same image, same size just a different scale or size.
D is not a dilation because the baby duck is not just a smaller replication as the mother duck since it is not the same size.

8. Scale Factor and Center of Dilation
When we describe dilations we use the terms scale factor
Scale factor
Here we have Igor. He is 3 feet tall and the greatest width across his body is 2 feet.
He wishes he were 6 feet tall with a width of 4 feet.
Scale Factor - change in size of the object.
Center of Dilation – the very central point of the object.
He wishes he were larger by a scale factor of 2.

9. Scale factor > 1 0 < Scale Factor < 1 Scale Factor
If the scale factor is larger than 1, the figure is enlarged.
If the scale factor is between 1 and 0, the figure is reduced in size.
Scale factor > 1
The length of each side of the new image is equivalent to the length of the corresponding side of the original figure multiplied by the scale factor.
0 < Scale Factor < 1

10. Are the following enlarged or reduced??
Scale factor of 1.5
Discuss slides before clicking for the answer.
A is enlarged.
B is reduced.
C is enlarged.
D is reduced. D
Scale factor of 3 B
Scale factor of 0.75
Scale factor of 1/5

11. The Object and the Image
The original figure is called the object and the new figure is called the image.
The object is labeled with letters.
The image may be labeled with the same letters followed by the prime symbol.
Image
Object

12. Let’s Try Some Dilations
Graph
ABC 10 A’
Point A (3,4)
Point B (3,2)
Point c (5,2)
A’(6,8) x2 8 x2
B’(6,4) 6 C’ B’ A 4
C’(10,4) x2 B C 2
Now let’s dilate by scale factor 2!! 2 4 6 8 10

16. If the figure below is dilated using a scale factor of
what will be the coordinates of A’? A

17. If the figure below is dilated using a scale factor of
what will be the coordinates of A’? A