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LESSON 3.2
PROOF AND PERPENDICULAR LINES
LESSON 3.2 OBJECTIVES
• Develop a Flow Proof
• Prove results about perpendicular lines
• Use Algebra to find angle measure
WARM-UP: GIVE A REASON
(a)
(b)
If =, then  (Def. of Cong. Angles)
If lin pair, then supp. (Def. of a linear pair)
(c)
If midpoint, then segs  (Def. of a midpoint)
(d)
If bisector, then s  (Def. of a bisector)
PROOFS IN CHAPTER 3
• In chapter 3 we will be proving statements about
perpendicular and parallel lines
• We will still use the two-column proof format (although
there are two others discussed in your text)
• You have a NEW proofs reference sheet for chapter 3
(also has some reasons from chapter 2 that we still need)
FLOW PROOF
5
6
7
• A flow proof uses arrows to show the flow of a
logical argument.
• Each reason is written below the statement it justifies.
GIVEN:  5 and  6 are a linear pair
 6 and  7 are a linear pair
PROVE:  5   7
 5 and  6
are a linear
pair
 6 and 
7 are a
linear pair
Given
1.  5 and  6 are a linear pair
 6 and  7 are a linear pair
1. Given
2.  5 and  6 are supplementary
 6 and  7 are supplementary
2. Linear Pair
Postulate
3.  5   7
3. Congruent
Supplements
Theorem
 5 and  6
Given
 6 and  7
are
supplementary
are
supplementary
Linear Pair
Postulate
 5 7
Linear Pair
Postulate
Congruent Supplements Theorem
THEOREM 3.1:
CONGRUENT ANGLES OF A LINEAR
PAIR
• If two lines intersect to form a linear pair of
congruent angles, then the lines are
perpendicular.
g
h
So g  h
THEOREM 3.2:
ADJACENT ANGLES COMPLEMENTARY
• If two sides of two adjacent acute angles are
perpendicular, then the angles are
complementary.
THEOREM 3.3: FOUR RIGHT ANGLES
• If two lines are perpendicular, then they intersect
to form four right angles.
COMPLETE THE PROOF
Given: 1  2
Statement
1  2
ml
Prove: m  l
Reason
Given
Theorem 3.1:
Congruent Angles of a
Linear Pair
COMPLETE THE PROOFS
Given: AB  AC
Prove: 1 & 2 are comp.
Statement
AB  AC
1 & 2
are comp.
Reason
Given
Theorem 3.2: Adjacent
Angles Complementary
COMPLETE THE PROOFS
Given: 1, 2, 3, 4 are right s
Prove: p  q
Statement
1, 2, 3, 4
are right s
pq
Reason
Given
Theorem 3.3: Four Right
Angles
SOLVE FOR X
Given: p  q
2x + x =90
3x = 90
X=30 °
D
C
A
B
SOLVE FOR X
Given: p  q
(2x +18) + 90 = 180
2x + 108 = 180
2x= 72
X=36
HOMEWORK
• 3.2 (pg. 139-140)
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