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

Name: __________________________________________ Date: ______________________ Period: ____ Weekly Homework 8 th Show all of your work to get credit. MONDAY 1.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 = 184x = 13.56x = 13.6

2 - d6h c² k² - 24k + 12 x -8 x -21 x -12

Transformations: Dilations

What is a Dilation?  Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure.

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

Which of these are dilations?? A C D B HINT: SAME SHAPE, DIFFERENT SIZE

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. He wishes he were larger by a scale factor of 2.

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 0 < Scale Factor < 1

Are the following enlarged or reduced?? A C D B Scale factor of 0.75 Scale factor of 3 Scale factor of 1/5 Scale factor of 1.5

The Object and the Image A’ A B B’ C’ C  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. Object Image

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

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

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