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Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)
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1 Lesson Plan #61 Date: Monday February 27th, 2017 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 # 61: 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. 5 Proof of the Angle Angle Similarity Theorem: Given: οABC and οDEF with οA ο οD and οB ο οE Prove: οABC 1) 2) 3) οDEF Statements οDEF οA ο ο D , οB ο ο E οC ο οF οABC and 4) Let G be a point on DE so that AB ο DG ( s. ο s.) 5) Let H be a point on DF so that AC ο DH ( s. ο s.) οABC ο οDGH οB ο οG οE ο οG 9) GH EF 6) 7) 8) DG DH ο½ DE DF 11) AB ο½ DG , AC ο½ DH AB AC ο½ 12) DE DF 10) β¦Do same to produce proportion with the other side If enough time: 1) Reasons 1) Given 2) Given 3) If two angles of one triangle are congruent, respectively to two angles of another triangle, then the third angles are congruent. (1, 2) 4) A line segment may be copied. 5) A line segment may be copied 6) s.a.s. ο s.a.s (4.2,5) 7) Corresponding parts of congruent triangles are congruent (6) 8) Transitive property of congruence (2,7) 9) If two coplanar lines are cut by a transversal forming congruent corresponding angles, then the lines are perpendicular. (8) 10) If a line is parallel to one side of a triangle and intersects the other two sides, then line divides the sides proportionally. (9) 11) Definition of congruent line segments. (4,5) 12) Substitution Postulate (10, 11) 6 3) 4) 5)