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Objectives: • Use properties of isosceles and equilateral triangles • Use properties of right triangles Properties of Isosceles Triangles vertex angle • In lesson 4.1, you learned that a triangle is an isosceles if it has at least two congruent sides. B • The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle. leg leg base angles A base C Remember: A • An EQUILATERAL triangle is a special type of isosceles triangle. B C Equilateral and Isosceles Triangles a. b. Find the value of x Find the value of y 3x = 180 X = 60 x° y° Ex. 2: Using Equilateral and Isosceles Triangles a. b. Find the value of x Find the value of y 120° + 2y° = 180° 2y = 60 y = 30 x° 60° y° Using Properties of Right Triangles • You have learned four ways to prove that triangles are congruent. • • • • Side-Side-Side (SSS) Side-Angle-Side (SAS) Angle-Side-Angle (ASA) Angle-Angle-Side (AAS) Solve: Solution: Isosceles Triangle X = 180-54-54 X=72 Solve: Solution: Two Isosceles Triangles 1. 90- 28 = 62 2. 180-62-62 = 56 3. X=56 Solve: Solution: Two Isosceles Triangles 1. 180 – 65-65 = 50 2. 180 – 50-50 = 80 3. X= 80 65 50 50 =80 50 Solve: Solution: 1. 120 = 60+60 2. 60= 60 vertical angles 3. X = 60 60 60 60 60 60 Try this one: Solution: 12 = 2x -12 24 = 2x X = 12 One More: Solution: 1. 180-68-68 = 44 2. 90 - 44 = 46 3. 4x – 2 = 46 Solve for x 4x = 48 X = 12 44 68 Last One: Solution: 1. 146 = 13x + 3 2. 143 = 13x 3. 11