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Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)
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1 Lesson Plan #49 Date: Thursday December 19th, 2013 Class: Geometry Topic: Similar Polygons Aim: What are the properties of similar polygons? Objectives: 1) Students will students will know the properties of polygons that are similar. HW # 49: Pg. 250 #βs 2-26 (Even number exercises only) Do Now 1) B E D 2) If < π΅π·πΈ β < π΅π΄πΆ, prove that π΅πΈ: πΈπΆ = π΅π·: π·π΄ C Statements A Reasons PROCEDURE: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Go over the Do Now Assignment #1: Examine the two polygons at right. What can you state about the two polygons? Assignment #2: Examine the two pairs of polygons at below. How do these polygons compare to the pair in assignment #1? What makes each pair of polygons in assignment #2 dissimilar? 2 Definition: Two polygons are similar if their vertices can be paired so that 1) Corresponding angles are congruent 2) Corresponding sides are in proportion The symbol for similarity is ~. What is the ratio of the lengths of any two corresponding sides in the similar polygons at right? Definition: The ratio of similitude of two similar polygons is the ratio of the lengths of any two corresponding sides; sometimes also referred to as the scale factor. Question: Is similarity of polygons an equivalence relation? Why? 3 Online Interactive Activity: Letβs go to http://www.mathopenref.com/similartriangles.html Online Interactive Activity: Letβs go to http://www.mathopenref.com/similaraaa.html Theorem: Two triangles are similar if two angles of one triangle are congruent to two corresponding angles of the other. Example #1: Statements Example #2: Example #3: Reasons 4 Example #4: Μ Μ Μ Μ Given: βπ΄π΅πΆ and βπ·π΅πΈ Μ Μ Μ Μ π·πΈ β₯ π΄πΆ Prove: βπ΄π΅πΆ~βπ·π΅πΈ Statements Reasons Theorem: A line that is parallel to one side of a triangle and intersects the other two sides in different points cuts off a triangle similar to the given triangle.