Perpendicular Theorems

1. 3.6 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
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 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
Bellwork
1/2 sheet (1. 2. 1. 2 side)

3. 3.6 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
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
4 3

4. 3.6 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
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 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
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 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
HW
pg. 194
#2­10
& 15­17

7. 3.6 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
BEL
L
WORK

8. 3.6 Perpendicular Theorems
Example
(7,2) Step 1: Find slope of 1st line.
HW pg. 194 #2­10,
15­17
October 02, 2014
Distance from a Point to a Line: length of perpendicular segment
from point to the line.
A
B
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
2 √
Distance Formula: (x2 ­x1
)2 + (y2 ­y1)
What is the distance between the two parallel lines?
(4,6)
(0,3)
(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.

9. 3.6 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014

10. 3.6 Perpendicular Theorems
HW pg. 194 #2­10,
15­17
October 02, 2014
Class Assignment
pg. 195
#23­27