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Transcript
Isosceles Triangles Tutorial 12f Isosceles Triangles • The congruent sides of an isosceles triangle are the legs. • The third side of an isosceles triangle is the base. • The two congruent sides form the vertex angle. • The other two angles are base A angles. B C Legs = AB, BC Vertex Angle = B Base = AC Base Angles = A, C Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. C A If AC BC, then A B B Bisector Theorem • The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. C If AC BC, and CD bisects ACB, then CD AB and CD bisects AB A D B Converse of Isosceles Triangle Theorem • If two angles of a triangle are congruent, then the sides opposite the angles are congruent. C A If A B, then AC BC B Corollary to Isosceles Triangle Theorem • If a triangle is equilateral, then it is equiangular. If XY YZ ZX, then X Y Z Y X Z Corollary to Converse of Isosceles Triangle Theorem • If a triangle is equiangular, then it is equilateral. If X Y Z, then XY YZ ZX Y X Z Click here to Check your answers x = 39 y = 90 x = 62 y = 28 x = 67 y = 67 x = 31 y = 31 x = 79 y = 90 x = 64 y = 26