Download Section 3.2 Day 1 Proof and Perpendicular Lines

Week 1
Warm Up
10.18.11
State the postulate or theorem:
1)
If 3 + 4 = 7, then 7 = 3 + 4,
2)
If 2x + 5 = 17, then 2x = 12.
3)
If ∠A and ∠B are vertical angles,
then ∠A ≅ ∠B.
Geometry
3.2 Day 1
Theorem
3.1
I will prove results about perpendicular lines.
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
Ex 1
Prove
T3.1
Given: ∠ 1 ≅ ∠ 2
Given: ∠ 1 and ∠ 2
2
1
are linear pairs
Prove: g ⊥ h
Step
∠1≅∠2
∠ 1 and ∠ 2 are linear pairs
m∠ 1 + m∠ 2 = 180º
m∠ 1 = m∠ 2
m∠ 1 + m∠ 1 = 180º
2m∠ 1 = 180º
Reason
Given
Given
Definition of Linear Pairs
Definition of congruent angles
Substitution property of equality
Simplify
m∠ 1 = 90º
Division property of equality
m∠ 2 = 90º
Substitution property of equality
∠ 1and ∠ 2 are right angles
g⊥h
Definition of right angles
Definition of perpendicular lines
Theorem
3.2
Perpendicular Adjacent Acute Angles
If two sides of two adjacent acute angles are
perpendicular, then the angles are
complementary.
Ex
90º
Theorem
3.3
Four Right Angles
If two lines are perpendicular, then they intersect
to form four right angles.
Ex
90º
Theorem
3.3
Four Right Angles
If two lines are perpendicular, then they intersect
to form four right angles.
Ex
90º
90º
90º
90º
Ex 2
j ⊥ k
What can you conclude?:
k
j
8
7
10
9
1) ∠ 7 and ∠ 8 are complementary
2) ∠ 9 is a right angle
3)
4)
Review
Do: 1
A _______ is a line that intersects two or more
coplanar lines.
What is the value of x?
65º
x
Assignment:
Handout - Section 3.2 B