5-Minute Check on Lesson 6-1

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Transparency 6-2
5-Minute Check on Lesson 6-1

• There are 480 sophomores and 520 juniors in a
  high school. Find the ratio of juniors to
  sophomores.
• A strip of wood molding that is 33 inches long is
  cut into two pieces whose lengths are in the
  ratio of 74. What are their lengths?
• Solve each proportion.
• 3.
• 4.
• 5.
• 6. The
  ratio of the measures of the three angles of a
  triangle is 13617. Find the measure of the
  largest angle.

1312
21 and 12 inches
6 72 --- --- x 84
x 7
39 4x --- ---- 57 19
x 13/4 3.25
2x 1 x 4 -------- --------- 4
8
x 2
Standardized Test Practice
85
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Lesson 6-2

• Similar Polygons

3
Objectives

• Identify similar figures
• Solve problems involving scale factors

4
Vocabulary

• Scale factor the ratio of corresponding sides
  of similar polygons

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Similar Polygons
R
Congruent Corresponding Angles m?A m?P m?B
m?Q m?C m?R m?D m?S
A
C
B
P
S
D
Corresponding Side Scale Equal AC AB
CD DB ---- ---- ---- ---- PR
PQ RS SQ
Q
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Example 1a
Determine whether the pair of figures is similar.
Justify your answer.
The vertex angles are marked as 40º and 50º, so
they are not congruent. Since both triangles are
isosceles, the base angles in each triangle are
congruent. In the first triangle, the base angles
measure ½ (180 40) or 70 and in the second
triangle, the base angles measure ½ (180 50) or
65
Answer None of the corresponding angles are
congruent, so the triangles are not similar.
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Example 1b
Determine whether the pair of figures is
similar.Justify your answer.
Since the measures of all the corresponding
angles are equal, then the angles must be
congruent.
Answer The ratio of the measures of the
corresponding sides are equal and the
corresponding angles are congruent, so ?ABC
?RST
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Example 1c
Determine whether the pair of figures is
similar.Justify your answer.
Answer Only one pair of angles are congruent,
so the triangles are not similar.
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Example 2a
An architect prepared a 12-inch model of a
skyscraper to look like a real 1100-foot
building. What is the scale factor of the model
compared to the real building?
Before finding the scale factor you must make
sure that both measurements use the same unit of
measure.
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Example 2b
A space shuttle is about 122 feet in length. The
Science Club plans to make a model of the space
shuttle with a length of 24 inches. What is the
scale factor of the model compared to the real
space shuttle?
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Example 3a
The two polygons are similar. Write a similarity
statement. Then find x, y, and UV.
Use the congruent angles to write the
corresponding vertices in order.
To find x
Similarity proportion
Multiply.
Divide each side by 4.
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Example 3a cont
To find y
Similarity proportion
Cross products
Multiply.
Subtract 6 from each side.
Divide each side by 6 and simplify.
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Example 3b
The two polygons are similar. Find the scale
factor of polygon ABCDE to polygon RSTUV.
The scale factor is the ratio of the lengths of
any two corresponding sides.
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Example 3c
The two polygons are similar.
a. Write a similarity statement. Then find a, b,
and ZO. b. Find the scale factor of polygon
TRAP to polygon ZOLD .
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Summary Homework

• Summary
• In similar polygons, corresponding angles are
  congruent, and corresponding sides are in (the
  same ratio) proportion
• The ratio of two corresponding sides in two
  similar polygons is the scale factor
• Homework
• pg 293-5 4, 6, 7, 12, 13, 27-31, 36, 38