Download 3.3 Parallel Lines & Transversals

Please pick up the yellow
warm-up and get to work
Parallel Lines &
Transversals
(quick review)
Slope &
Midpoints
Special Angle Relationships
Interior Angles
1
3 4
2
<3 & <6 are Alternate Interior angles
<4 & <5 are Alternate Interior angles
<3 & <5 are Same Side Interior angles
<4 & <6 are Same Side Interior angles
5 6
7 8
Exterior Angles
<1 & <8 are Alternate Exterior angles
<2 & <7 are Alternate Exterior angles
<1 & <7 are Same Side Exterior angles
<2 & <8 are Same Side Exterior angles
Special Angle Relationships
WHEN THE LINES ARE
PARALLEL
1
3
5
2
4
6
7 8
If the lines are not
parallel, these angle
relationships DO
NOT EXIST.
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are
CONGRUENT
♥Same Side Interior Angles are
SUPPLEMENTARY
♥Same Side Exterior Angles are
SUPPLEMENTARY
Let’s Practice
120°1
60°3
120° 5
7
60°
2 60°
4 120°
6 60°
8 120°
m<1=120°
Find all the remaining
angle measures.
Another practice problem
40°
120°
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.
Slope and Midpoints
Slope is the steepness of line.
Given 2 points, you can find the slope:
y2 – y1
x2 – x1
A midpoint is the point in the middle of a line
segment.
Given 2 points, you can find the middle:
M = x1 + x2 , y1 + y 2
2
2
(
)
Example
What is the slope and midpoint of the line
segment that contains the points (-3,-1) and
(3,3)?
Slope:
m = 3 – (-1) = 4 = 2
3 – (-3)
6
3
Midpoint:
(
M = -3 + 3 , 3 + (-1)
2
2
)
=
0 ,2
2
2
=
(0 , 1)
Parallel lines have the same slope
Perpendicular lines have negative
reciprocal slopes
Lines that have unrelated slopes are
neither parallel nor perpendicular
hmmm..
For instance, given these
vertices of a triangle, how could
I tell if it was a right triangle?
(1, 2), (3, 3), (4, 0)
1/2
-3
2/-3
guess this is
not a right
triangle
I would have to find the
slopes of all the sides
(yes, that means, you
may have to find 3
slopes)
And see if 2 slopes are
the negative reciprocal of
each other.
How could I use
slope to tell if a
triangle had a
right angle?
Assignment
* Practice wksht 3.3 A & B
* Wksht pg 194, 6-28