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Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)
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1 Lesson Plan #47 Date: Monday December 19th, 2011 Class: Geometry Topic: Similar Polygons Aim: What are the properties of similar polygons? Objectives: 1) Students will students will know that properties of polygons that are similar. HW # 47: Pg. 250 #’s 2-26 (Even number exercises only) Do Now 1) The diagonals of an isosceles trapezoid A) are congruent b) bisect each other C) are perpendicular D) form 4 congruent angles. 2) ̅̅̅̅ ? What is the length of 𝑉𝐶 1 A) 3.5 B) 7 C) 14 7 B D) 24 E D 3) If < 𝐵𝐷𝐸 ≅< 𝐵𝐴𝐶, prove that 𝐵𝐸: 𝐸𝐶 = 𝐵𝐷: 𝐷𝐴 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: Let’s go to http://www.mathopenref.com/similartriangles.html Online Interactive Activity: Let’s 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 ̅̅̅̅ Given: ∆𝐴𝐵𝐶 and ∆𝐷𝐵𝐸 ̅̅̅̅ 𝐷𝐸 ∥ 𝐴𝐶 Prove: ∆𝐴𝐵𝐶~∆𝐷𝐵𝐸 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.