Download Similar Polygons Notes and Practice

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Notes and Practice
Similar Polygons
Identify Similar Polygons Similar polygons have the same shape but not necessarily the same size.
Example 1: If △ABC ∼ △XYZ, list all pairs of congruent angles and write a proportion that relates the
corresponding sides.
Use the similarity statement.
Congruent angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z
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Proportion:
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Example 2: Determine whether the pair of figures is similar. If so, write the similarity statement and scale factor.
Explain your reasoning.
Step 1 Compare corresponding angles.
∠W ≅ ∠P, ∠X ≅ ∠Q, ∠Y ≅ ∠R, ∠Z ≅ ∠S
Corresponding angles are congruent.
Step 2 Compare corresponding sides.
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WXYZ ∼ PQRS. The polygons are similar with a scale factor of .
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Exercises
List all pairs of congruent angles, and write a proportion that
relates the corresponding sides for each pair of similar
polygons.
1. △DEF ∼ △GHJ
2. PQRS ∼ TUWX
Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor.
If not, explain your reasoning.
3.
Chapter 7
4.
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Glencoe Geometry
NAME ____________________________________________ DATE _____________________________ PERIOD _____________
7-2 Study Guide and Intervention (continued)
Similar Polygons
Use Similar Figures You can use scale factors and proportions to find missing side lengths in similar polygons.
Example 1: The two polygons are similar. Find x and y.
Example 2: If △DEF ∼ △GHJ, find the scale factor of
△DEF to △GHJ and the perimeter of each triangle.
The scale factor is
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The perimeter of △DEF
is 10 + 8 + 12 or 30.
Use the congruent angles to write the corresponding
vertices in order.
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△RST ∼ △MNP
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Write proportions to find x and y.
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32y = 38(16)
x = 26
y = 19
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(3)(30) = 2x
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16x = 32(13)
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45 = x
Theorem 7.1
Substitution
Cross Products Property
Solve.
So, the perimeter of △GHJ is 45.
Exercises
Each pair of polygons is similar. Find the value of x.
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5. If ABCD ∼ PQRS, find the scale factor of ABCD
to PQRS and the perimeter of each polygon.
Chapter 7
13
Glencoe Geometry