1. Week 1 Warm Up 10.18.11 1) If 3 + 4 = 7, then 7 = 3 + 4,
State the postulate or theorem:
1) If = 7, then 7 = 3 + 4,
2) If 2x + 5 = 17, then 2x = 12.
Add theorem 2.1 here next year.
3) If ∠A and ∠B are vertical angles,
then ∠A ≅ ∠B.

2. Geometry
3.2 Day 1
I will prove results about perpendicular lines.
Theorem 3.1
Linear Pairs of Congruent Angles
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular Ex
g ⊥ h

3. 1 2 Ex 1 Prove T3.1 Given: ∠ 1 ≅ ∠ 2 Given: ∠ 1 and ∠ 2
are linear pairs
Prove: g ⊥ h
Step
Reason
∠ 1 ≅ ∠ 2
Given
∠ 1 and ∠ 2 are linear pairs
Given
m∠ 1 + m∠ 2 = 180º
Definition of Linear Pairs
m∠ 1 = m∠ 2
Definition of congruent angles
m∠ 1 + m∠ 1 = 180º
Substitution property of equality
2m∠ 1 = 180º
Simplify
m∠ 1 = 90º
Division property of equality
m∠ 2 = 90º
Substitution property of equality
∠ 1and ∠ 2 are right angles
Definition of right angles
g ⊥ h
Definition of perpendicular lines

4. Perpendicular Adjacent Acute Angles
Theorem 3.2
Perpendicular Adjacent Acute Angles
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Ex
90º

5. Theorem 3.3
Four Right Angles
If two lines are perpendicular, then they intersect to form four right angles. Ex
90º

6. Theorem 3.3
Four Right Angles
If two lines are perpendicular, then they intersect to form four right angles.
90º Ex

7. k j Ex 2 What can you conclude?: j ⊥ k 8 9 7 10
1) ∠ 7 and ∠ 8 are complementary
2) ∠ 9 is a right angle 3) 4)

8. What is the value of x? 65º x Review
A _______ is a line that intersects two or more coplanar lines.
Do: 1
What is the value of x?
65º
Add theorem 2.1 here next year. x
Assignment:
Handout - Section 3.2 B