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.

base angles

vertex angle

base

legleg

B

A C

Remember:

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

A

B C

Equilateral and Isosceles Triangles

a. Find the value of xb. Find the value of y

3x = 180X = 60

x°

y°

Ex. 2: Using Equilateral and Isosceles Trianglesa. Find the value of xb. Find the value of y

120° + 2y° = 180°2y = 60 y = 30

x°

y°60°

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 TriangleX = 180-54-54X=72

Solve:

Solution:Two Isosceles

Triangles1.90- 28 = 622.180-62-62 = 563.X=56

Solve:

Solution:Two Isosceles

Triangles1.180 – 65-65 = 502.180 – 50-50 = 803.X= 80

65

50

50

50=80

Solve:

Solution:1.120 = 60+602.60= 60 vertical

angles3.X = 60

60

60

60

60

60

Try this one:

Solution:12 = 2x -1224 = 2xX = 12

One More:

Solution:1.180-68-68 = 442.90 - 44 = 463.4x – 2 = 46Solve for x4x = 48X = 12

44

68

Last One:

Solution:1.146 = 13x + 32.143 = 13x3.11