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Geometry Notes G.6 Isosceles, Equilateral Triangles Mrs. Grieser Name: _____________________________________________ Date: ______________ Block: ________ Isosceles and Equilateral Triangles Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem If two angles of a triangle are congruent, the sides opposite them are congruent. Corollary to the Base Angles Theorem If a triangle is equilateral, then it is equiangular. Corollary to the Converse of the Base Angles Theorem If a triangle is equiangular, then it is equilateral. Examples a) Given RT ST . Name two congruent angles. b) Find AB and AC in the triangle at right. c) In the diagram find: 1) WY 2) mWXY d) mDEF 90 . Find values of x and y. e) 1) What post. can be used to prove that ABC AED ? f) Find the values of x and y. 2) Explain why ACD is equiangular. 3) Show that ABD AEC . Each angle in an equiangular triangle measures _______ Geometry Notes G.6 Isosceles, Equilateral Triangles g) Find the values of x and y. h) Given: BD bisects ADC ; DB AC Prove: ADC is isosceles Statements Reasons 1)________________ 1) Given 2) _______________ 2) Definition of < bisector 3) 3 4 3) ____________________ 4) DB DB 4) ____________________ 5) ______________ 5) ASA 6) ______________ 6) CPCTC 7) ADC is isosceles 7) _____________________ Mrs. Grieser Page 2