1) The document discusses key theorems about parallel and perpendicular lines including: if two lines intersect to form congruent angles then they are perpendicular; if two lines are perpendicular they intersect to form four right angles; and if two sides of two adjacent acute angles are perpendicular then the angles are complementary. 2) It also discusses the perpendicular transversal theorem which states that if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other line. 3) The document provides instructions for homework problems involving parallel and perpendicular lines and finding the distance between parallel lines.

1. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 1
October 02, 2013
Oct 7­1:55 PM
Bellwork
1. Write an equation of the line in slope-intercept form.
y = 4x - 3
2. Write an equation of the line passing through the point (2, -3)
that is parallel to the line y = 6x + 4. y = 6x -15
3. Graph 2x - 3y = -12.

2. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 2
October 02, 2013
Oct 2­7:47 AM
Bellwork
pg. 198
construct parallel and
perpendicular lines

3. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 3
October 02, 2013
Oct 7­2:06 PM
3.6 Prove Theorems about Perpendicular Lines
Theorem 3.8: If 2 lines intersect to form a linear pair of congruent angles,
then the lines are perpendicular.
If <1 ≅ <2, then g h. 1 2
Theorem 3.9: If 2 lines are perpendicular,
then they intersect to form 4 right angles.
If a b, then <1,<2,<3 & <4 are right <s.
1 2
34

4. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 4
October 02, 2013
Oct 7­3:11 PM
Theorem 3.10: If 2 sides of 2 adjacent acute angles are perpendicular,
then the angles are complementary.
1
2
If BA BC, then <1 & <2 are complementary.

5. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 5
October 02, 2013
Oct 7­3:16 PM
Theorem 3.11: Perpendicular Transversal Theorem
If a transversal is to 1 of 2 // lines,
then it is to the other line.
h
k
j
If h // k and j h, then j k.
Theorem 3.12: Lines Perpendicular to a Transversal Theorem
If 2 lines are to the same line,
then they are // to each other.
If m p & n p, then m // n.
m n
p

6. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 6
October 02, 2013
Oct 7­4:06 PM
HW
pg. 194
#2­10 & 15­17

7. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 7
October 02, 2013
Oct 13­7:30 AM
B
E
L
L
W
O
R
K

8. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 8
October 02, 2013
Oct 8­10:06 AM
Distance from a Point to a Line: length of perpendicular segment
from point to the line.
B
A
k
Distance between 2 Parallel Lines: length of any perpendicular
segment joining the 2 lines.
m
p
C
D
Distance btwn point A & line k = AB
Distance btwn line p & line m = CD
Distance Formula: (x2 ­ x1)2 + (y2 ­ y1)2 √
What is the distance between the two parallel lines?
(4,6)
(0,3)
(3,­1)
(7,2)
Step 1: Find slope of 1st line.
Step 2: Write equation of 1st line.
Step 3: Write equation of line to 1st line through 2nd line
Step 4: Find intersection of 1st line and line.
Step 5: Find distance between // lines using point of intersection and the
chosen point from step 3.
Example

9. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 9
October 02, 2013
Oct 8­12:30 PM

10. 3.6 Prove Parallel & Perpendicular Theorems
HW pg. 194 #2­10, 15­17 10
October 02, 2013
Oct 11­1:25 PM
Class Assignment
pg. 195
#23­27