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Transcript
December 11, 2014 Questions December 11, 2014 Isosceles Triangles What does it mean for a triangle to be isosceles? Parts of an Isosceles Triangle vertex angle base angles base Isosceles Triangle Symmetry Theorem The line containing the bisector of the vertex angle of an isosceles triangle is a symmetry line for the triangle Isosceles Triangle Coincidence Theorem In an isosceles triangle, the bisector of the vertex angle, the perpendicular bisector of the base, and the median to the base determine the same line. - bisector of vertex angle - symmetry line - perpendicular bisector of base - median to the base Isosceles Triangle Base Angles Theorem If a triangle has two congruent sides, then the angles opposite them are congruent. Equilateral Triangle Symmetry Theorem Every equilateral triangle has three symmetry lines, which are bisectors of its angles (or equivalently, the perpendicular bisectors of the sides). Equilateral Triangle Angle Theorem If a triangle is equilateral, then it is equiangular. Corollary Each angle of an equilateral triangle has measure 60º. December 11, 2014 Examples 1. In ⊙Z below, m∠ZXY = 31º. What is the measure of m∠XZY? X Z Y A 2. Given: AB = AC in ∆ABC Prove: m∠3 = m∠4 1 3 B 2 C 4 3. Is it possible for a triangle to have exactly two symmetry lines? Explain. December 11, 2014 Assignment: p. 313 (2-9, 12-18 even)