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Geo.11.21.14 4.2.notebook November 21, 2014 Warm Up Classify each triangle. 4-2 Isosceles Triangles p. 142 Objective: Use and apply properties of isosceles triangles. 1 Geo.11.21.14 4.2.notebook November 21, 2014 Isosceles Triangle vertex angle -- 2 congruent sides leg leg base angle base angle base Theorem 4-1 Isosceles Triangle Thm If 2 sides of a triangle are congruent, then the angles opposite the sides are congruent. C If AC = BC, then A B 2 Geo.11.21.14 4.2.notebook November 21, 2014 Examples: y 55° 40° x x Theorem 4-3 Converse of the Isosceles Triangle Thm If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. If < A = < B, then C A B 3 Geo.11.21.14 4.2.notebook November 21, 2014 Examples: x-4 x 15 9 4 Geo.11.21.14 4.2.notebook November 21, 2014 Theorem 4-2 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. C A B Examples: 63° y C B A A x° C x y 20° B C 20° A x° y B 5 Geo.11.21.14 4.2.notebook November 21, 2014 Corollary to Isosceles Triangle Thm If a triangle is equilateral, then it is equiangular. Corollary to Converse of the Isosceles Triangle Thm If a triangle is equiangular, then it is equilateral. 6 Geo.11.21.14 4.2.notebook November 21, 2014 Examples: 32 x x y° 13 HW # 39 p. 191-92 # 1-15, 22-25 ** Draw diagram when needed! 7