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Chapter 8 Lesson 2

Chapter 8 Lesson 2. Objective: To identify similar polygons. Similar Polygons. Notes Two figures that have the same shape but not necessarily the same size are similar (~). Two figures are similar if: Corresponding angles are congruent Corresponding sides are proportional.

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Chapter 8 Lesson 2

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  1. Chapter 8 Lesson 2 Objective: To identify similar polygons.

  2. Similar Polygons Notes • Two figures that have the same shape but not necessarily the same size are similar (~). • Two figures are similar if: • Corresponding angles are congruent • Corresponding sides are proportional • The ratio of the lengths of corresponding sides is the similarity ratio.

  3. B C 53° A D F G 127° E H Example 1: Understanding Similarity ABCD ~ EFGH. Complete each statement. a. = 53 Corresponding angles are congruent. b. Corresponding sides are proportional.

  4. Example 2: Understanding Similarity ∆ABC ~ ∆XYZ. Complete each statement. a. = 78 B Corresponding angles are congruent. b. A C Corresponding sides are proportional. Y 78° 42° X Z

  5. Example 3: Determining Similarity Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio. • Remember: • Two figures are similar if: • Corresponding angles are congruent • Corresponding sides are proportional All three pairs of angles are congruent by the markings. ∆ABC ~ ∆FED Similarity Statement 3 : 4 or ¾ Similarity Ratio

  6. Example 4: Determining Similarity Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio. Y • Remember: • Two figures are similar if: • Corresponding angles are congruent • Corresponding sides are proportional 12 14 X Z 16 All three pairs of angles are congruent by the markings. N 18 21 P M 24 ∆XYZ ~ ∆MNP Similarity Statement 2 : 3 or 2/3Similarity Ratio

  7. Example 5: Determining Similarity Determine whether the parallelograms are similar. Explain. K L 1 2 B C 120° 100° They are not similar because corresponding angles are not congruent. 2 2 4 4 A D J M 1 2

  8. Example 6:Using Similar Figures LMNO ~ QRST. Find the value of x. Step 1: Write a proportion. Step 2: Substitute. Step 3: Cross Multiply.

  9. Example 7:Using Similar Figures LMNO ~ QRST. Find the value of SR. Step 1: Write a proportion. Step 2: Substitute. Step 3: Cross Multiply.

  10. Assignment

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