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Transcript
Applied Geometry Lesson: 6 – 4 Isosceles Triangles Objective: Learn to identify and use properties of isosceles triangles. Parts of an Isosceles Triangle Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite the sides are congruent. Theorem 6-3 The median from the vertex angle of an isosceles triangle lies on the perpendicular bisector of the base and the angle bisector of the vertex angle. x = 49 y = 90 Because EG is also a perpendicular bisector. x = 65 y = 50 x = 90 y = 70 Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. mB 48 mA mB mC 180 48 48 mC 180 mC 84 4x = 6x - 5 AC = 4(2.5) = 10 -2x = -5 x = 2.5 BC = 6(2.5) -5 = 10 mC 84 AC 10 BC 10 Theorem 6-5 A triangle is equilateral if and only if it is equiangular. Homework Pg. 249 1 – 5 all, 6 – 22 E
