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Understanding and Identifying Similar Polygons

In this lesson, we explore the concept of similar polygons, where two figures share the same shape but may differ in size. We'll identify key characteristics that define similarity, such as congruent corresponding angles and proportional corresponding sides. You'll learn how to write similarity statements and calculate the similarity ratio. Through engaging examples, we will determine whether pairs of polygons are similar based on their corresponding angles and sides, consolidating your understanding of these principles.

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Understanding and Identifying Similar Polygons

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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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