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Section 4.3 Isosceles and Equilateral Triangles Objective β’ SWBAT use properties of isosceles and equilateral triangles to find angle measures and side lengths Isosceles Triangles The congruent sides of an isosceles triangle are called legs The other side is called the base The two angles at the base are called the base angles Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite of them are congruent Symbols: If π΄π΅ β π΄πΆ, then <C β <B Base Angles Theorem Find the value of the missing angle x = 55° x = 68° x = 45° Converse of the Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. Symbols: If <B β <C, then π΄πΆ β π΄π΅ Use the Converse of the Base Angles Theorem Find the value of x By the Converse to the Base Angles Theorem DE = DF x + 3 = 12 - 3 -3 x=9 You Try Find the value of y y = 50° y=9 y = 12 Equilateral Triangles If a triangle is equilateral, then it is equiangular. Symbols: If π΄π΅ β π΄πΆ β π΅πΆ , then < π΄ β < π΅ β < πΆ If a triangle equiangular, then it is equilateral. Symbols: If < π΄ β < π΅ β < πΆ, then π΄π΅ β π΄πΆ β π΅πΆ Equilateral Triangles Find the length of each side of the equiangular triangle. QR = QT by the equiangular theorem 3x = 2x + 10 -2x -2x x =10 3(10) = 30 Equilateral Triangles Find the value of x. 2y + 5 = 4y - 3 by the equilateral theorem -2y -2y 5 = 2y - 3 +3 +3 8 = 2y __ __ 2 2 y=4 You Try! Find the value of y y=7 y=5