1. 3.6 Perpendicular Theorems October 01, 2012
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.
Oct 7­1:55 PM
HW pg. 194 #2­10, 15­17 1

2. 3.6 Perpendicular Theorems October 01, 2012
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.
1 2
If <1 ≅ <2, then g h.
Theorem 3.9: If 2 lines are perpendicular,
then they intersect to form 4 right angles.
1 2
If a b, then <1,<2,<3 & <4 are right <s.
4 3
Oct 7­2:06 PM
HW pg. 194 #2­10, 15­17 2

3. 3.6 Perpendicular Theorems October 01, 2012
Theorem 3.10: If 2 sides of 2 adjacent acute angles are perpendicular,
then the angles are complementary.
If BA BC, then <1 & <2 are complementary. 1
2
Oct 7­3:11 PM
HW pg. 194 #2­10, 15­17 3

4. 3.6 Perpendicular Theorems October 01, 2012
Theorem 3.11: Perpendicular Transversal Theorem
If a transversal is to 1 of 2 // lines,
then it is to the other line.
j
h
If h // k and j h, then j k.
k
Theorem 3.12: Lines Perpendicular to a Transversal Theorem
If 2 lines are to the same line,
then they are // to each other.
m n
If m p & n p, then m // n. p
Oct 7­3:16 PM
HW pg. 194 #2­10, 15­17 4

5. 3.6 Perpendicular Theorems October 01, 2012
HW
pg. 194
#2­10 & 15­17
Oct 7­4:06 PM
HW pg. 194 #2­10, 15­17 5

6. 3.6 Perpendicular Theorems October 01, 2012
B
E
L
L
W
O
R
K
Oct 13­7:30 AM
HW pg. 194 #2­10, 15­17 6

7. 3.6 Perpendicular Theorems October 01, 2012
Distance from a Point to a Line: length of perpendicular segment
from point to the line.
A
Distance btwn point A & line = AB
k
k
B
Distance between 2 Parallel Lines: length of any perpendicular
segment joining the 2 lines.
C m
Distance btwn line & line m = CD
p
p
D
Distance Formula: (x2 ­ x1)2 + (y2 ­ y1)2
√
Example
What is the distance between the two parallel lines?
(4,6)
Step 1: Find slope of 1st line. (0,3) (7,2)
(3,­1)
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.
Oct 8­10:06 AM
HW pg. 194 #2­10, 15­17 7

8. 3.6 Perpendicular Theorems October 01, 2012
Oct 8­12:30 PM
HW pg. 194 #2­10, 15­17 8

9. 3.6 Perpendicular Theorems October 01, 2012
Class Assignment
pg. 195
#23­27
Oct 11­1:25 PM
HW pg. 194 #2­10, 15­17 9