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4-5:Isosceles and Equilateral Triangles Properties of Isosceles Triangles Vertex Leg Vertex: the meeting of the two equal legs Leg Base: opposite vertex angle Base Angle Base Base Angle Base Angles: opposite the equal legs 1 Theorem 4‐3: Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Theorem 4‐4: Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Complete Got It? #1 p. 251 Theorem 4‐5: If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base. Complete Got It? #2 p. 252 x 63 2 Corollary to Theorem 4‐3: A If a triangle is equilateral, then the triangle is equiangular. C B Corollary to Theorem 4‐4: A If a triangle is equiangular, then the triangle is equilateral. C B Ex. 1: B Given: AB BC Prove: BAC ECD A Statement Justification C D E 3 Ex. 2 In circle P below, mP 37. What is mPAB ? 180 37 143 71.5 2 37° P B A Ex. 3 In isosceles triangle ABC below, mB 118 and the bisectors of angles A and C intersect at point E. Find mAEC. 180 118 62 31 2 2 31 15.5 2 180 15.5 2 180 31 149 A C 15.5 15.5 149 E 118 B 4 Homework: p. 254 #6‐12 even, 22, 23, 25, 27, 28, 30‐ 32, 37‐40. 5