Similar Polygons

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Similar Polygons

• Chapter 7-2

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Lesson 2 MI/Vocab

• Identify similar figures.

• Solve problems involving scale factors.

• similar polygons

• scale factor

Standard 11.0 Students determine how changes in
dimensions affect the perimeter, area, and volume
of common geometric figures and solids.
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Similar Polygons

• Have congruent corresponding angles.
• Have proportional corresponding sides.
• means is similar to

ABCD EFGH ?A ? ?E ?B ? ?F ?C ? ?G ?D ? ?H
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Writing Similarity Statements

• Decide if the polygons are similar. If they are,
  write a similarity statement.

?A ? ?W ?B ? ?Y ?C ? ?Z ?D ? ?X
All corr. sides are proportionate and all corr.
angles are ? ABCD WYZX
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Scale Factor

• The ratio of the lengths of two corresponding
  sides.
• In the previous example the scale factor is 32.

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Lesson 2 Ex1
Similar Polygons
A. Determine whether each pair of figures is
similar. Justify your answer.
The vertex angles are marked as 40º and 50º, so
they are not congruent.
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Lesson 2 Ex1
Similar Polygons
Answer None of the corresponding angles are
congruent, so the triangles are not similar.
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Lesson 2 Ex1
Similar Polygons
B. Determine whether each pair of figures is
similar. Justify your answer.
All the corresponding angles are congruent.
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Lesson 2 Ex1
Similar Polygons
Now determine whether corresponding sides are
proportional.
The ratios of the measures of the corresponding
sides are equal.
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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Lesson 2 CYP1
A. Determine whether the pair of figures is
similar.
A. Yes, ?AXE ?WRT. B. Yes, ?AXE ?RWT. C. No,
the ?'s are not . D. not enough information
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Lesson 2 CYP1
B. Determine whether the pair of figures is
similar.
A. Yes, ?TRS ?NGA. B. Yes, ?TRS ?GNA. C. No,
the ?'s are not . D. not enough information
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Lesson 2 Ex2
ARCHITECTURE 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. 1 foot 12 inches
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Lesson 2 Ex2
AnimationSimilar Polygons
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Lesson 2 CYP2
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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Lesson 2 Ex3
Proportional Parts and Scale Factor
A. 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. polygon ABCDE
polygon RSTUV
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Lesson 2 Ex3
Proportional Parts and Scale Factor
Now write proportions to find x and y.
To find x
Similarity proportion
Cross products
Multiply.
Divide each side by 4.
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Lesson 2 Ex3
Proportional Parts and Scale Factor
To find y
Similarity proportion
AB 6, RS 4, DE 8, UV y 1
Cross products
Multiply.
Subtract 6 from each side.
Divide each side by 6 and simplify.
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Lesson 2 Ex3
Proportional Parts and Scale Factor
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Lesson 2 Ex3
Proportional Parts and Scale Factor
B. 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.
Answer
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Lesson 2 CYP3
A. The two polygons are similar. Write a
similarity statement.
A. TRAP OZDL B. TRAP OLDZ C. TRAP
ZDLO D. TRAP ZOLD
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Lesson 2 CYP3
B. The two polygons are similar. Solve for a.
A. a 1.4 B. a 3.75 C. a 2.4 D. a 2
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Lesson 2 CYP3
C. The two polygons are similar. Solve for b.
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Lesson 2 CYP3
D. The two polygons are similar. Solve for ZO.
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Lesson 2 CYP3
E. The two polygons are similar. What is the
scale factor of polygon TRAP to polygon ZOLD?

1. A
2. B
3. C
4. D

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Lesson 2 Ex4
Enlargement or Reduction of a Figure
Rectangle WXYZ is similar to rectangle PQRS with
a scale factor of 1.5. If the length and width of
PQRS are 10 meters and 4 meters, respectively,
what are the length and width of rectangle WXYZ?
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Lesson 2 Ex4
Enlargement or Reduction of a Figure
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Lesson 2 CYP4
A. 9.8 in, 19.6 in B. 7 in, 14 in C. 6 in, 12
in D. 5 in, 10 in
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Lesson 2 Ex5
Scales on Maps
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Lesson 2 Ex5
Scales on Maps
Solve
Cross products
The distance across the city is 30 miles.
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Lesson 2 Ex5
Scales on Maps
Divide each side by 10.
It would take Tashawna 3 hours to bike across
town.
Examine To determine whether the answer is
reasonable, reexamine the scale. If 0.25 inches
2 miles, then 4 inches 32 miles. The distance
across the city is approximately 32 miles. At 10
miles per hour, the ride would take about 3
hours. The answer is reasonable.
Answer 3 hours
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Lesson 2 CYP5
An historic train ride is planned between two
landmarks on the Lewis and Clark Trail. The scale
on a map that includes the two landmarks is 3
centimeters 125 miles. The distance between the
two landmarks on the map is 1.5 centimeters. If
the train travels at an average rate of 50 miles
per hour, how long will the trip between the
landmarks take?
A. 3.75 hr B. 1.25 hr C. 5 hr D. 2.5 hr
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Homework

• Chapter 7-2
• Pg 392
• 1 6, 8 11, 14 19,
• 28 36, (9th and 10th grade),
• 37 41, 60 64 evens, 71 76

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Forced Perspective