1. Proof and Perpendicular Lines
Chapter 3 Section 3.2
Proof and Perpendicular Lines

2. Warm-Up

3. 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 

4. Three New Theorems
Thm 3.2 If two sides of adjacent acute angles are perpendicular,
then the angles are complementary 1 2
Lines   1 and 2 are complementary

5. 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

6. State the reason for the conclusion
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

7. State the reason for the conclusion
Given: 5   6
Conclusion: 6  5
Symmetric Prop
4. Given: x is the midpoint of
Conclusion:
Def. Midpoint

8. State the Reason for the Conclusion
Given: bisects BAC
Conclusion: BAD  DAC
Definition Angle Bisector

9. Find the value of x x + 38 = 90 x = 52 x –12 + 49 = 90 x + 37 = 90

10. Find the value of x
x + 3x = 90
4x = 90
x =

11. Complete the Two-column Proof of Theorem 3.2
Statements Reasons
1. Given
2. Def.  Lines
3. mDCE = 90
4. Segment Addition Post
= m1 + m2
6. Def. Complementary Angles

12. Definition Vertical Angles
Vertical Angle Theorem
def.  Angles
Given
Def. Right Angle
Substitution