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Transcript
November 10, 2016 Unit 4, Lesson 6 Isosceles Triangle Theorem "Mighty is geometry; joined with art, resistless." - Euripides Example 1: A A (hint: What is a congruence statement we can write?) B C B C November 10, 2016 Example 2: A A C B B How are Examples 1 and 2 related? What is true if a triangle has two congruent sides? What if two angles are congruent? C November 10, 2016 Isosceles Triangle Theorem ( Theorems 4-1 and 4-2) Two sides of a triangle are congruent if and only if the angles opposite those sides are congruent. Parts of an Isosceles Triangle: Legs - two congruent sides Base - the third side Base Angles - Angles formed with base Vertex Angle - Angle opposite base November 10, 2016 Corollary 1 to Isos. Triangle Theorem A triangle is equilateral if and only if it is equiangular Corollary 2 to Isos. Triangle Theorem o An equilateral triangle has three 60 angles. November 10, 2016 Corollary 3 to Isos. Triangle Theorem The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. Example 3: Find the measure of angle A. November 10, 2016 Example 4: Find the measure of angle BOC. O is the center of the circle. (hint: what do you know about the radii of a circle, and let Example 5: ) November 10, 2016 Example 6: Explain why all equilateral triangles are isosceles triangles but not all isosceles triangles are equilateral triangles.