Download Math 2 Honors Name__________________________ Lesson 4

Math 2 Honors
Lesson 4-2: Similar Figures
Name__________________________
Date _______________________
Learning Goals:
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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:
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If 2 figures are congruent, then their corresponding lengths are ______________ & their corresponding
angles are _______________.
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If 2 figures are similar, then their corresponding lengths are ___________________ & their
corresponding angles are _______________.
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Scale Factor: The ratio of any two corresponding lengths in two similar geometric figures.
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Notation: A scale factor of 3, can be as S3.
PART 1: COORDINATE GEOMETRY & SIMILARITY
Quadrilateral WXYZ is graphed at the right.
W  (4, 6), X  (5, 4), Y  (2, 6), and Z  (5,1)
1. List the coordinates of the vertices of the
image of WXYZ under S1.5 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
y  y1
.
( x1 , y1 ) and ( x2 , y2 ) : slope  2
x2  x1
3. Find the distance from the origin to W and from the origin to W ' .
Distance = ( x2  x1 )2  ( y2  y1 )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 S0.75 and graph it.
X '' 
W '' 
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 R ' S 'T ' ?
14. What is the ratio of the triangles areas?
area of R ' S ' T '
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
the area of its image?
1
is performed on a figure with an area of 8 units, what would be
2
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,
X ' Y ' Z ' is a size-change image of
22. Is this size change an expansion (k > 1),
or a contraction (k <1)? _______________
23. If X 'Y '  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 Y ' Z '  6.4.
XYZ
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?
28. What is the ratio of the volumes?
image
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?