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Section 4.7: Isosceles and Equilateral Triangles Understand the relationship between Sides and Angles in Isosceles and Equilateral Triangles and be able to use that relationship to solve problems. Vocabulary of Isosceles Triangles Vertex Angle Leg Leg Base Angles Theorem 4.7: Base Angles Theorem. β’ If two Sides of a triangle are congruent, then the Angles opposite them are Congruent. OR β’ If the Legs of an Isosceles Triangle are congruent then the Base Angles must be congruent. A Leg Leg Base Angles If π¨π© β π¨πͺ, then β π© β β πͺ B C Theorem 4.7: Base Angles Theorem J Proof Statements 1. π½πΎ β π½πΏ 2. M is Midpoint of πΎπΏ 3. Draw π½π K L 4. πΎπ β πΏπ Given: βπ½πΎπΏ, π½πΎ β π½πΏ 5. π½π β π½π Prove: β π β β π 6. βπ½πΎπ β βπ½πΏπ 7. β πΎ β β πΏ Reasons 1. Given 2. Def. of Midpoint 3. 2 points determine a line 4. Def. of Midpoint 5. Reflexive Property 6. SSS 7. CPCTC Theorem 4.8: Converse Base Angles Theorem. β’ If two Angles of a triangle are congruent, then the Sides opposite them are Congruent. OR β’ If the Base Angles of an Isosceles Triangle are congruent then the Legs must be congruent. A Leg Leg Base Angles If β π© β β πͺ, then π¨π© β π¨πͺ B C This is the Transamerica Building. You need to reproduce the pyramid on the top of the building to create a logo for the Transamerica Corp. The information you have been given is that the angle at the lower right hand corner of the pyramid is approximately 85°. In order to create a logo that visually matches the building you will need to find the measure of the other two angles. Describe your method: Equilateral Triangles Base Angles Corollary β’ If two congruent sides means two congruent angles, then three congruent sides must mean three congruent angles Corollaries: Equilateral Triangles β’ Corollary to the Base Angles Theorem: If a Triangle is equilateral, then it is equiangular. Why must this be true? β’ Corollary to the Converse Base Angles Theorem: If a Triangle is equiangular, then it is equilateral. Homework 4.7 p.267 # 1,3,6,9,12,15,18,21