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Transcript
4-5 Isosceles and Equilateral Triangles Objectives Students will be able to Use and apply properties of isosceles and equilateral triangles Essential Understanding The angles and sides of isosceles and equilateral triangles have special relationships Isosceles Triangles What are some things you know about isosceles triangles? The congruent sides are called the legs Third side is the base The two congruent legs form the vertex angle The other two angles are the base angles Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Example 1 Is <WVS congruent to <S? Explain Is TR congruent to TS? Explain Will triangle RUV is isosceles? Explain Theorem If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base. Example What is the value of x? Example Corollary to Isosceles Triangle Thm Corollary: a theorem that can be proved easily using anther theorem If a triangle is equilateral, then the triangle is equiangular Corollary to Converse of Isosceles Triangle Thm If a triangle is equiangular, then the triangle is equilateral Example If I have and equilateral triangle, what are the measures of the angles of that triangle? Homework Pg. 254 – 256 6 – 12 even, 16 – 20, 22, 25, 28, 30, 32 14 problems