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5.4 Equilateral & Isosceles Triangles Goals: β’ Use the Base Angle Theorem β’ Use isosceles & equilateral triangles Using the Base Angles Theorem: A triangle is isosceles when it has at least two congruent sides. When an isosceles triangle has exactly two congruent sides, these two sides are the legs. The angle formed by the legs is the vertex angle. The third side is the base of the isosceles triangle. The two angles adjacent to the base are called base angles. Using the Base Angles Theorem: Base Angles Theorem: If two sides of a triangle are congruent, the angles opposite of them are congruent. If π΄π΅ β π΄πΆ, then β π΅ β β πΆ. Using the Base Angles Theorem: Converse of the Base Angles Theorem: If two angles of a triangle are congruent, then the sides opposite of them are congruent. Ifβ π΅ β β πΆ, then π΄π΅ β π΄πΆ. Example 1: Using the Base Angles Theorem If βπ·πΈπΉ, π·πΈ β π·πΉ. Name two congruent angles. You Try! 1. If π»πΊ β π»πΎ, then β ______ β β ______. 2. If β πΎπ»π½ β β πΎπ½π», then ______ β _______. Using the Base Angles Theorem: 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. Example 2: Finding the Measures in a Triangle Find the measures of β π, β π, and β π . You Try! Find the length of ππ for the triangle. Example 3: Using Isosceles & Equilateral Triangles Find the values of x and y in the diagram. You Try! . Find the values of x and y in the diagram.