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Transcript
4.5 Isosceles and Equilateral Triangles Isosceles Triangles •At least two sides are of equal length. •It also has two congruent angles. Vertex Angle Legs Base Base Angles Isosceles Triangle Theorem If two sides of a triangle are congruent, the angles opposite them are congruent. IF : AB AC THEN : B C Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, the sides opposite them are congruent IF : B C THEN : AB AC The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base CD AB and CD bisects AB Corollary to Theorem 4.3 If a triangle is equilateral, then the triangle is equiangular x X Y Z Y Z Corollary to Theorem 4.4 If a triangle is equiangular, then the triangle is equilateral x XY YZ ZX Y Z