3.4: Parallel Lines and the Triangle
Angle-Sum Theorem
Inconceivable!
Inconceivable!
-Vizzini
Finding Angle Measures in Triangles
C
50°
A
35°
B
Finding Angle Measures in Triangles
C
50°
35°
A
B
Theorem 3-12: Triangle Angle-Sum Theorem:
The sum of the measures of the angles of a triangle is 180.
mA  mB  mC  180

Finding Angle Measures in Triangles
Finding Angle Measures in Triangles
G
Find the values of x, y, and z.
39°
21°
65° x° y° z°
F
J
H
Finding Angle Measures in Triangles
B
Find the values of x, y, and z.
x°y°
z° 49°
62°
A
C
D
Classifications of Triangles
Equiangular
All 's are 
Acute
All 's acute

Equilateral
All sides 
Right
One right 
Obtuse
One obtuse 


Isosceles
At least 2 sides 
Scalene
No sides 
Classifications of Triangles
Classify the following triangles by their angles and sides.
37°
37°
Draw an equilateral right triangle.
NOT POSSIBLE!!!
Using Exterior Angles of Triangles
Exterior Angle of a Polygon: An angle formed by a side and an
extension of an adjacent side.
Exterior
Angle
2
1
3
Remote
Interior
Angles
Remote Interior Angles: The two nonadjacent interior angles
corresponding to each exterior angle of a triangle.
Using Exterior Angles of Triangles
100°
x°
50°
Using Exterior Angles of Triangles
2
1
3
Theorem 3-13: Triangle Exterior Angle Theorem:
The measure of each exterior angle of a triangle equals the sum
of the measures of its two remote interior angles.
m1  m2  m3

Using Exterior Angles of Triangles
Find the values of w, x, y, and z.
x°
97°
y°
53°
w°86° z°
Little Mo’ Practice
Find the value of x.
(80 – 2x)°
(70 – 3x)°
3.4: Parallel Lines
and the Triangle
Angle-Sum
Theorem
HOMEWORK: 3.4: #2-26 even, 32, 34, 40
THT: 1-5, 7, 9
QUIZ ON MONDAY ON 3.1-3.4!!!!
TERMS: equiangular Δ, acute Δ, right Δ, obtuse Δ,
equilateral Δ, isosceles Δ, scalene Δ.
Remember, with
with great
great power,
power, comes
comes great
great responsibility.
responsibility.
Remember,
-Uncle Ben