Chapter 3
Section 3.2
Proof and Perpendicular Lines
Warm-Up
Three New Theorems
Thm 3.1
If two lines intersect to form a
linear pair of congruent angles,
then the lines are perpendicular
1
2
1  2  lines are 
Three New Theorems
Thm 3.2 If two sides of adjacent acute
angles are perpendicular,
then the angles are complementary
Lines   1 and 2 are complementary
1
2
Three New Theorems
Thm 3.3 If two lines are perpendicular,
then they intersect to form 4 right angles
Lines   All 4 angles are right angles
State the reason for the conclusion
1. Given: m1 = m 2
Conclusion: 1  2
Def.  Angles
2. Given: 3 and 4 are a linear pair
Conclusion: 3 and 4 are Supplementary
Linear Pair Postulate
State the reason for the conclusion
3. Given: 5   6
Conclusion: 6  5
Symmetric Prop
4. Given: x is the midpoint of MN
Conclusion: MX  NX
Def. Midpoint
State the Reason for the Conclusion
5. Given: AD bisects BAC
Conclusion: BAD  DAC
Definition Angle Bisector
Find the value of x
6. x + 38 = 90
x = 52
7. x –12 + 49 = 90
x + 37 = 90
x = 53
Find the value of x
8. x + 3x = 90
4x = 90
90
45

x=
2
4
Complete the Two-column Proof
of Theorem 3.2
Statements
Reasons
1. Given
2. Def.  Lines
3. mDCE = 90
4. Segment Addition Post
5. 90 = m1 + m2
6. Def. Complementary Angles
A. Definition Vertical Angles
D. Given
B. Vertical Angle Theorem
E. Def. Right Angle
C. def.  Angles
F. Substitution
G. Def. Right Angle