Math 2 Honors Name__________________________
Lesson 4-2: Similar Figures Date _______________________
Learning Goals:

I can define and perform a dilation on a figure in the coordinate plane with a given center and scale factor.

I can define similarity as a composition of rigid motions following by dilations in which angle measure is preserved and side length is proportional.

I can identify corresponding sides and corresponding angles of similar triangles.

I can verify that when a side passes through the center of dilation, the side and its image lie on the same line.

I can verify that corresponding sides of the preimage and image are parallel.

I can verify that the side length of the image is equal to the scale factor multiplied by the corresponding side length of the preimage.
Congruent Figures Similar Figures
“Rough” definitions:
Notation:

If 2 figures are congruent , then their corresponding lengths are ______________ & their corresponding angles are _______________.

If 2 figures are similar , then their corresponding lengths are ___________________ & their corresponding angles are _______________.

Scale Factor: The ratio of any two corresponding lengths in two similar geometric figures.

Notation: A scale factor of 3, can be as S
3
.

PART 1: COORDINATE GEOMETRY & SIMILARITY
Quadrilateral WXYZ is graphed at the right.
W X
 
Y

(2, 6), and Z

(5,1)
1.
List the coordinates of the vertices of the image of WXYZ under S
1.5
and graph it.
W '

X '

Y '

Z '

2.
Write the equation of the line in y
 mx
 b form, from W to W '.
Remember for two points x y
1
) and (
2
,
2
) : slope
 y
2
 y
1 x
2
 x
1
.
3.
Find the distance from the origin to W and from the origin to W ' .
Distance =
( x
2
 x
1
)
2 
( y
2
 y
1
)
2
4.
What is the ratio of distance from origin to W '
? distance from origin to W
5.
List the coordinates of the vertices of the image of WXYZ under S
0.75
and graph it.
W ''

X ''

Y ''

Z ''

6.
Write the equation of the line in y
 mx
 b form, from W to W '' .
7.
What do you notice about the equations from number 2 and number 6?
8.
Find the distance from the origin to W and from the origin to W '' .
9.
What is the ratio of distance from origin to W ''
? distance from origin to W
10.
What is the significance of your answers for numbers 4 and 8?

PART 2: CONSTRUCTIONS, DILATIONS & CENTERS
11.
Draw the image of triangle RST under a size change with center C and magnitude 3.
12.
What is the area of triangle RST ?
13.
What is the area of triangle ' ' ' ?
14.
What is the ratio of the triangles areas? area of ' ' ' area of RST
15.
How is the ratio of the triangles areas related to the magnitude of the scale factor?
16.
If a dilation with a magnitude of 3 is performed on a figure with an area of 8 units, what would be the area of its image?
17.
If a dilation with a magnitude of
1
2
is performed on a figure with an area of 8 units, what would be the area of its image?

18.
If a dilation with a magnitude of k is performed on a figure with an area of A units, what would be the area of its image?
19.
Explain why your answer to number 17 makes sense.
20.
Draw the image of JKL under a size change with a center at K and a magnitude of 0.7.
21.
For the figure at the right, use a ruler to determine the center C and scale factor k for the size transformation represented. The image is shown by the dashed line.
In the figure at the right, ' ' ' is a size-change image of XYZ
22.
Is this size change an expansion ( k > 1),
or a contraction ( k <1)? _______________
23.
If ' ' 10 and XY

8, find the magnitude k of the size change.
24.
Use the value of k from number 22 to find YZ if ' '

6.4.

PART 3: CONSTRUCTIONS & PROPORTIONALITY
25.
Draw the image of the rectangular prism below using a scale factor of 0.6 and center C .
26.
What is the volume of the prism? (pre-image)
27.
What is the volume of the image? image
28.
What is the ratio of the volumes? pre-image
29.
How is the ratio of the volumes related to the magnitude of the scale factor?
30.
If a dilation with a magnitude of 3 is performed on a figure with a volume of 8 units, what would be the volume of its image?