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The Isosceles Triangles Theorems Section 4-6 Isosceles Triangle Theorem If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. 8 8 50 50 Proof of Theorem 4.9 Isosceles Triangle Theorem Proof of Theorem 4.9 Isosceles Triangle Theorem Theorem 4-10 If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent. Corollaries 4.3 and 4.4 A triangle is equilateral if and only if it is equiangular. Each angle of an equilateral triangle measures 60 degrees. 12 60 12 60 60 12 Parts of an Isosceles Triangle vertex angle leg base base angles leg The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. Joke Time Who was the first math student? Add-em Why isn’t your nose 12 inches long? Because then it would be a foot