Transcript Theorems about Parallel Lines

Proofs & Perpendicular Lines
Sec. 3.2 p. 136
GOALS:
To learn the characteristics of three different
types of proofs
To write a paragraph proof
To learn theorems on perpendicular lines
Theorems 3.1 & 3.2
Theorem 3.1
If lines g and h form a linear pair of  angles,
then g  h
g
h
Theorem 3.2
If 2 sides of adj. acute 's are  ,
then the 2 's are complementary.
1
2
Theorem 3.3
Theorem 3.3
If two lines are perpendicular, then they intersect to form four right
angles.
m
l
Examples
Which theorem or postulate justifies the following given
that the lines are perpendicular?
1)
m5  m6  90
6
5
m
2)
3 & 4 are right angles
3
4
l
Two-Column Proof
of Theorem 3.2
A
Given: BA  BC
Prove: 1 & 2 are complementary
2
B
Statements
1. BA  BC
2. ABC is a right angle
3. mABC  90
4. m1  m2  mABC
5. m1  m2  90
6. 1& 2 are comp.
Reasons
1
C
1. Given
2. Defn. of  lines or
 lines form a right 
3. Defn. or rt.  or
a right  has a measure of 90
4. Angle Addn. Post.
5. Substitution Prop.
6. Defn. of comp. 's
Three types of Proofs & Characteristics
1. Two column proof:
•
Most formal
•
Lists numbered statements in left column and a reason for
each statement in the right column
2. Paragraph proof:
•
Describes the logical argument with sentences
•
More conversational
3. Flow proof:
•
Uses the same statements and reasons as a twocolumn proof, but the logical flow connecting the
statements is indicated by arrows
See notes sheet for an example of the three
types of proofs!