Objectives Use properties of isosceles and equilateral triangles

Objectives: • Use properties of isosceles and equilateral triangles • Use properties of right triangles

Properties of Isosceles Triangles • In lesson 4. 1, you learned that a triangle is an isosceles if it has at least two congruent sides. • The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle.

Remember: • An EQUILATERAL triangle is a special type of isosceles triangle.

Equilateral and Isosceles Triangles a. b. Find the value of x Find the value of y 3 x = 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° + 2 y° = 180° 2 y = 60 y = 30 x° 60° y°

Using Properties of Right Triangles • You have learned four ways to prove that triangles are congruent. • • Side-Side (SSS) Side-Angle-Side (SAS) Angle-Side-Angle (ASA) 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

Try this one: Solution: 12 = 2 x -12 24 = 2 x X = 12

One More: Solution: 1. 180 -68 -68 = 44 2. 90 - 44 = 46 3. 4 x – 2 = 46 Solve for x 4 x = 48 X = 12 44 68

Last One: Solution: 1. 146 = 13 x + 3 2. 143 = 13 x 3. 11