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4.7 Use Isosceles and Equilateral Triangles Goal Use theorems about isosceles and equilateral triangles. VOCABULARY Legs - The legs of an isosceles triangle are the two congruent sides. Legs Vertex angle - The vertex angle of an isosceles triangle is the angle formed by the legs. Base - The base of an isosceles triangle is the side that is not a leg. Base angles - The base angles of an isosceles triangle are the two angles adjacent to the base. Base s BASE ANGLES THEOREM If two sides of a triangle are congruent, then the angles opposite them are congruent. If then If AB AC , then B ____. CONVERSE OF BASE ANGLES THEOREM If two angles of a triangle are congruent, then the sides opposite them are congruent. If then If B C, then AB _____. Example Apply the Base Angles Theorem In FGH, FH GH . Name two congruent angles. COROLLARY TO THE BASE ANGLES THEOREM If a triangle is equilateral, then it is _____________. COROLLARY TO THE CONVERSE OF BASE ANGLES THEOREM If a triangle is equiangular, then it is _____________. The corollaries state that a triangle is equilateral if and only if it is equiangular. = sides = s Example Find measures in a triangle Find the measures of R, S, and T. (All sides are =, so all s are =) Examples Use isosceles and equilateral triangles Find the values of x and y. Find the values of x and y in the diagram.