1. 7-2 Ratios in Similar Polygons
HW On The Corner of Your Desk!
Drill #3.12 2/20/13
1. If ∆QRS ∆ZYX, identify the pairs of
congruent angles and the pairs of congruent
sides. Q Z; R Y; S X;
QR ZY; RS YX; QS ZX
Solve each proportion.
2. 3.
x=9 x = 18
Holt McDougal Geometry

2. 7-2 Ratios in Similar Polygons
Lesson Review
1. The ratio of the angle measures in a triangle is
1:5:6. What is the measure of each angle?
15°, 75°, 90°
Solve each proportion.
2. 3 3. 7 or –7
4. Given that 14a = 35b, find the ratio of a to b in
simplest form.
5. An apartment building is 90 ft tall and 55 ft
wide. If a scale model of this building is 11 in.
wide, how tall is the scale model of the building?
18 in.
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3. 7-2 Ratios in Similar Polygons
Objectives
Identify similar polygons.
Apply properties of similar polygons to
solve problems.
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4. 7-2 Ratios in Similar Polygons
Vocabulary
similar
similar polygons
similarity ratio
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5. 7-2 Ratios in Similar Polygons
Figures that are similar (~) have the same shape
but not necessarily the same size.
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6. Proving Similar Triangles
• Are the triangles similar?
15
12
16 20
18
24

7. 7-2 Ratios in Similar Polygons
Two polygons are
similar polygons if
and only if their
corresponding angles
are congruent and their
corresponding side
lengths are
proportional.
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8. Are these similar?
6
2
1 18
5

9. Scale Factor
The ratio of the lengths
of two corresponding
sides of similar
polygons.

10. 7-2 Ratios in Similar Polygons
Example 1: Describing Similar Polygons
Identify the pairs of
congruent angles and 0.5
corresponding sides.
N Q and P R.
By the Third Angles Theorem, M T.
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11. 7-2 Ratios in Similar Polygons
Check It Out! Example 1
Identify the pairs of
congruent angles and
corresponding sides.
B G and C H.
By the Third Angles Theorem, A J.
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12. 7-2 Ratios in Similar Polygons
A similarity ratio is the ratio of the lengths of
the corresponding sides of two similar polygons.
The similarity ratio of ∆ABC to ∆DEF is , or .
The similarity ratio of ∆DEF to ∆ABC is , or 2.
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13. 7-2 Ratios in Similar Polygons
Writing Math
Writing a similarity statement is like writing a
congruence statement—be sure to list
corresponding vertices in the same order.
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14. 7-2 Ratios in Similar Polygons
Example 2A: Identifying Similar Polygons
Determine whether the polygons are similar.
If so, write the similarity ratio and a
similarity statement.
rectangles ABCD and EFGH
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15. 7-2 Ratios in Similar Polygons
Example 2A Continued
Step 1 Identify pairs of congruent angles.
A E, B F, All s of a rect. are rt. s
C G, and D H. and are .
Step 2 Compare corresponding sides.
Thus the similarity ratio is , and rect. ABCD ~ rect. EFGH.
Holt McDougal Geometry

16. 7-2 Ratios in Similar Polygons
Example 2B: Identifying Similar Polygons
Determine whether the
polygons are similar. If
so, write the similarity
ratio and a similarity
statement.
∆ABCD and ∆EFGH
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17. 7-2 Ratios in Similar Polygons
Example 2B Continued
Step 1 Identify pairs of congruent angles.
P R and S W isos. ∆
Step 2 Compare corresponding angles.
m W = m S = 62°
m T = 180° – 2(62°) = 56°
Since no pairs of angles are congruent, the triangles
are not similar.
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18. 7-2 Ratios in Similar Polygons
Check It Out! Example 2
Determine if ∆JLM ~ ∆NPS.
If so, write the similarity
ratio and a similarity
statement.
Step 1 Identify pairs of congruent angles.
N M, L P, S J
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19. 7-2 Ratios in Similar Polygons
Check It Out! Example 2 Continued
Step 2 Compare corresponding sides.
Thus the similarity ratio is , and ∆LMJ ~ ∆PNS.
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20. 7-2 Ratios in Similar Polygons
Helpful Hint
When you work with proportions, be sure the
ratios compare corresponding measures.
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21. 7-2 Ratios in Similar Polygons
Example 3: Hobby Application
Find the length of the model
to the nearest tenth of a
centimeter.
Let x be the length of the model
in centimeters. The rectangular
model of the racing car is similar
to the rectangular racing car, so
the corresponding lengths are
proportional.
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22. 7-2 Ratios in Similar Polygons
Example 3 Continued
5(6.3) = x(1.8) Cross Products Prop.
31.5 = 1.8x Simplify.
17.5 = x Divide both sides by 1.8.
The length of the model is 17.5 centimeters.
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23. 7-2 Ratios in Similar Polygons
Check It Out! Example 3
A boxcar has the dimensions shown.
A model of the boxcar is 1.25 in. wide. Find
the length of the model to the nearest inch.
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24. 7-2 Ratios in Similar Polygons
Check It Out! Example 3 Continued
1.25(36.25) = x(9) Cross Products Prop.
45.3 = 9x Simplify.
5 x Divide both sides by 9.
The length of the model is approximately 5 inches.
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25. Perimeter of similar polygons
• The ratio of the
perimeters of two
similar polygons is
the same as the ratio
of the corresponding
sides

26. 7-2 Ratios in Similar Polygons
Lesson Quiz: Part I
1. Determine whether the polygons are similar. If so,
write the similarity ratio and a similarity
statement.
no
2. The ratio of a model sailboat’s dimensions to the
actual boat’s dimensions is . If the length of the
model is 10 inches, what is the length of the
actual sailboat in feet?
25 ft
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27. 7-2 Ratios in Similar Polygons
Lesson Quiz: Part II
3. Tell whether the following statement is
sometimes, always, or never true. Two equilateral
triangles are similar.
Always
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