Parallel Lines and the Triangle AngleSum Theorem

1
Section 3.3

• Parallel Lines and the Triangle Angle-Sum Theorem

2
Definitions

• Types of Triangles by Angle
• Equiangular all angles are ?
• Acute all angles acute
• Right one angle is 90
• Obtuse one angle is gt 90

3
Definitions

• Types of Triangles by Sides
• Equilateral all sides are ?
• Isosceles two sides are ?
• Scalene no sides are ?

4
Theorem 3-7Triangle Angle-Sum Theorem

• The sum of the measures of the angles of a
  triangle is 180
• m? A m? B m? C 180

C
B
A
5
Using Algebra for Theorem 3-7

• G
• F J H

• ? GFJ
• 39 65 x 180
• 104 x 180
• x 76
• ? FJH
• x y 180
• 76 y 180
• y 104
• ? GJH
• 21 104 z 180
• 125 z 180
• z 55

39
21
65
x
y
z
Find x, y, and z
6
Theorem 3-8Triangle Exterior Angle Theorem

• The measure of each exterior angle of a triangle
  equals the sum of the measures of its two remote
  interior angles
• Symbolism m? 1 m? 2 m? 3

7
Using Algebra for Theorem 3-8

• angle A 40 30
• 70
• 113 70 angle B
• 43 angle B

40
A
30
113
70
B
8
Homework

• Page 134
• 2-10even, 26-36even, 40-48even, 62