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Unit Review
The problems in this unit helped you understand the concept of
similarity as it applies to geometric shapes. You learned how
•
•
•
to make similar shapes
•
to investigate the use of similarity to solve problems
to determine whether two shapes are similar
side lengths, perimeters, angle measures, and areas of similar shapes
relate to each other
Use Your Understanding: Similarity
Test your understanding of similarity by solving the following problems.
1. The square below is subdivided into six triangles and four
parallelograms. Some of the shapes are similar.
A
D
E
B
G
F
C
H
J
K
a. List all the pairs of similar triangles in the figure. For each pair,
give the scale factor from one figure to the other.
b. Pick a pair of similar triangles. Explain how their perimeters are
related and how their areas are related.
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c. List several pairs of triangles in the figure that are not similar.
d. List all pairs of similar parallelograms in the figure. For each pair,
give the scale factor from one figure to the other.
e. Pick a pair of similar parallelograms. Explain how their perimeters
are related and how their areas are related.
f. List several pairs of parallelograms in the figure that are not similar.
2. a. Suppose a triangle is on a coordinate grid. Which of the following
rules will change the triangle into a similar triangle?
i.
(3x, 3y)
iii. (2x, 4y)
v.
(1.5x, 1.5y)
ii. (x + 3, y + 2)
iv. (2x, 2y + 1)
vi. (x - 3, 2y - 3)
b. For each of the rules in part (a) that will produce a similar triangle,
give the scale factor from the original triangle to its image.
3. A school photograph measures 12 centimeters by 20 centimeters. The
class officers want to enlarge the photo to fit on a large poster.
a. Can the original photo be enlarged to 60 centimeters by
90 centimeters?
b. Can the original photo be enlarged to 42 centimeters by
70 centimeters?
Looking Back and Looking Ahead
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Explain Your Reasoning
Answer the following questions to summarize what you know.
4. What questions do you ask yourself when deciding whether two shapes
are similar?
5. Suppose shape A is similar to shape B. The scale factor from shape A
to shape B is k.
a. How are the perimeters of the two figures related?
b. How are the areas of the two figures related?
6. If two triangles are similar, what do you know about the following
measurements?
a. the side lengths of the two figures
b. the angle measures of the two figures
7. Tell whether each statement is true or false. Explain.
a. Any two equilateral triangles are similar.
b. Any two rectangles are similar.
c. Any two squares are similar.
d. Any two isosceles triangles are similar.
Look Ahead
You will study and use ideas of similarity in several future Connected
Mathematics units, especially where it is important to compare sizes and
shapes of geometric figures. Basic principles of similarity are also used in a
variety of practical and scientific problems where figures are enlarged or
reduced.
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