Sec' 34

1
Sec. 3-4

• Parallel Lines the Triangle Angle Sum Theorem

Objectives a) To classify triangles find the
measures of their angles. b) To use the
exterior angles of a triangle.
2
Th(3-7) Triangle Angle Sum Thm

• Says that every triangle has 180 in it.
• Regardless of its size or classification.

• Must construct the triangle such that AB // TS.

T
S
1
3
2
A
B
3
Proof
S
C
T
1
3
2
Given ?ABC TS // AB
A
B
Prove m?A m?B m?2 180

• Statements
• ?ABC TS // AB
• 2. m?1 m?3 m?2 180
• 3. m?1 m?A
• m?3 m?B
• 4. m?A m?B m?2 180

• Reasons
• Given
• Angle Add Post
• Alt. Interior Angles are ?
• 4. Subs.

4
Example 2 Find m?a m?b
m?c m?b 20 m?c 20 m?a
70
Example 1 Find the m?Z m?X m?Y m?Z
180 m?48 m?67 m?2 180 m?Z 65
Z
C
70
c
48
67
Y
X
a
b
A
D
B
5
I. Classify ?s by their Angles

• Right Triangle
• One ? is Rt. ( 90)
• The other 2 are Acute.

• Obtuse ?
• One ? is Obtuse ( gt 90)
• Other 2 are Acute.

gt 90

• Acute ?
• All ?s are acute ( lt90 )

6

• 4) Equiangular ?
• A special Acute ?
• All ?s must be acute
• All ?s must be ?
• 180/3 60
• Each ? must be 60

7
II. Classify ?s by their Sides

• Scalene ?
• No Sides ?
• No ?s ?

• 2) Isosceles ?
• _at_ least 2 sides are ?
• 2 ?s are ?, called base ?s

• Equilateral ?
• All sides are ?
• All ?s are ?
• Equilateral ?s are also Equiangular ?s

8
III. Using Exterior ?s of a ?
A
Exterior ? of a ?
Remote Interior ?s
Alt Int angles
B
C
9
Th(3-8) ? Exterior ? Thm.

• The measure of each Exterior ? of a triangle
  equals the sum of the measures of its two
  interior ?s.

3
4
2
m?1 m?2 m?3
3
4
1
10
Proof
C
2
Given ?1 is an exterior ? of ?ABC
Prove m?1 m?2 m?3
1
3
4
B
A

• Statements
• ?1 is an exterior ? of ?ABC
• m?1 m?4 180
• m?4 m?3 m?2 180
• m?1 m?4 m?4 m?3 m?2
• m?1 m?3 m?2

• Reasons
• Given
• ? add Postulate
• Def of ?
• Subs
• Subtr.

11
Example

• Solve for the m?1 in the following triangle.

Use the exterior ? thm 125 90 m?1 m?1 35
125
1
12
Example

• What type of triangle is ?ABC
• Classify it by its sides and its angles

C
m?A 90
45
Angles Right
45
B
A
Sides Isosceles
13
Example

• Whats wrong with this diagram?

Exterior ? must be greater than the remote
interior ?.
85?
80?
14
What have we learned??

• 180 in a ?
• The exterior ? equals the sum of the two remote
  interior ?s.
• Classify ?s by their
• Sides Scalene, Isosceles, or Equilateral
• ?s Right, Acute, Obtuse