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Understanding Similar Polygons: Congruent Angles and Proportional Sides

In this lesson, we explore the fundamental concepts of similar polygons, focusing on the properties that define their similarity: congruent corresponding angles and proportional lengths of corresponding sides. We'll examine various examples, including finding the scale factor between polygons and applying the similarity theorem. Additionally, we'll solve problems involving proportionality statements and scale factors. The provided exercises will reinforce your understanding of the topic, ensuring a solid grasp of similar polygons.

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Understanding Similar Polygons: Congruent Angles and Proportional Sides

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  1. Week 5 Warm Up 01.30.12

  2. Similar Polygons Corresponding angles are congruent and the lengths of corresponding sides are proportional. Ex 1 Statement of Proportionality

  3. Ex 2 Similarity Statement ∼ Symbol for Similar

  4. Theorem 8.1 K P L Q R N M S If KLMN ∼ PQRS Then, sides perimeters = = = =

  5. JKLM ∼ QPRS. Find the value of z. Ex 3 = 15z = 6( 10 ) 15z = 60 z = 4

  6. Scale Factor The ratio of the lengths of the corresponding sides. Scale factor of the pool to the patio is: 48ft : 32ft Scale factor = 3 : 2

  7. Ex 4 Statement of Proportionality TUVW ∼ ABCD Scale Factor 5 : 3 Length of TW 30 = 3x 10 = x 180 - 70 m∠TUV 110

  8. Find the value of x. Do: Assignment: Textbook page 461, 10 - 44 Evens and 45 – 50 all.

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