Download Section 3-3 Parallel Lines and the Triangle Angle

Section 3-3
Parallel Lines and the Triangle
Angle-Sum Theorem
Activity #1
Behold !
m1  m2  3  180
1
2
3
3
Activity #2
1
2
Behold !
m1  m2  3  180
3
2 1
3
Formal Proof
Given : ΔABC
Prove : m1  m4  5  180
A
2
D
1
4
C
3
Triangle Angle-Sum Theorem:
The sum of the measures of the
angles of a triangle is 180˚.
E
5
B
Statements
Reasons
1. ABC
1. Given
2. DE || BC
2. Parallel line postulate
(by constructi on)
3. DAE is a straight angle
3. Assumed from diagram
4. m1  m2  m3  mDAE
4. Angle addition postulate
5. mDAE  180
5. Def. straight 
6. m1  m2  m3  180
6. Substituti on
7. 2  4; 3  5
7. ||lines  alt. int. s 
8. m2  m4; m3  m5
9. m1  m4  m5  180
8. Def. 
9. Substituti on
Given : ΔABC
Prove : m2  m3  m4
Formal Proof
A
2
D
4
C
1
3
Triangle Exterior Angle
Theorem: The measure of each
exterior angle of a triangle
equals the sum of the measures
of its two remote interior
B angles.
Statements
Reasons
1. ABC
1. Given
2. m1  m2  m3  180
2. Triangle angle - sum theorem
3. DCB is a straight angle
3. Assumed from diagram
4. m1  m4  mDCB
4. Angle addition postulate
5. mDCB  180
5. Def. straight 
6. m1  m4  180
6. Substituti on
7. m1  m2  m3  m1  m4
7. Substituti on
8. m2  m3  m4
8. Subtraction POE
Classifying Triangles
Classify by Angles
60˚
60˚
60˚
Equiangular
Acute
Right
Classify by Sides
Equilateral
Isosceles
Scalene
Obtuse
Example 1
x
67˚
48˚
Example 2
z
x
70˚
y
Example 3:classify by angles and sides
5
2
120˚
4
Example 4:
125˚
X
Example 5:
A triangle with a 90˚ angle has
sides that are 3 cm, 4 cm, and 5
cm long. Classify the triangle by
its angles and sides.
Example 6:
y
70˚
42˚
Example 7:
90˚
76˚
x
Example 8:
2x + 28
4x
32˚
Example 9:
5x + 40
10x
3x − 4
Example 10:
x
125˚
160˚