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Transcript
November 30, 2015 4.4 The Isosceles Triangle Theorems November 30, 2015 AB ⊥ BD, AB||DE, CF BISECTS AE AND BD A AB = DE F C D B What can you conclude? E November 30, 2015 4.4 Objectives 1) Apply the theorems and corollaries about isosceles triangles 2) Use the AAS Theorem to prove two triangles congruent 3) Use the HL Theorem to prove two right angles congruent 4) Prove that two overlapping triangles are congruent November 30, 2015 November 30, 2015 November 30, 2015 November 30, 2015 November 30, 2015 The Transamerica Pyramid in San Francisco Each of its four faces is an isosceles triangle, with two congruent sides. The congruent sides are called legs, and the third side is called the base. There are also two base angles and one vertex angle. base base angle leg vertex angle base angle leg Label the isosceles triangle. November 30, 2015 Theorem 4-1 The Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite to those sides are congruent. November 30, 2015 Three Corollaries based on Theorem 4-1 Corollary 1 An equilateral triangle is also equiangular. Corollary 2 An equilateral triangle has three 60˚ angles Corollary 3 The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. November 30, 2015 November 30, 2015 Theorem 4-2 If two angle of a triangle are congruent, then the sides opposite those angles are congruent. (Converse of Theorem 4-1) November 30, 2015 One Corollary based on Theorem 4-2 Corollary An equilateral triangle is also equilateral November 30, 2015 November 30, 2015 November 30, 2015 November 30, 2015 November 30, 2015 Proof November 30, 2015 November 30, 2015