1. Please pick up the yellow warm-up and get to work

2. Parallel Lines & Transversals (quick review) Slope & Midpoints

4. Special Angle Relationships
Interior Angles
<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 1 4 2 6 5 7 8 3
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

5. Special Angle Relationships WHEN THE LINES ARE PARALLEL
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are CONGRUENT
♥Same Side Interior Angles are SUPPLEMENTARY
♥Same Side Exterior Angles are SUPPLEMENTARY 1 4 2 6 5 7 8 3
If the lines are not parallel, these angle relationships DO NOT EXIST.

6. Let’s Practice m<1=120° Find all the remaining angle measures. 1 46 5 7 8 3
m<1=120°
Find all the remaining angle measures.
120°
60°
120°
60°
120°
60°
120°
60°

7. Another practice problem
40°
Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.
120°

8. ( ) 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 + y2
( )

9. 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)
Midpoint:
M = , 3 + (-1) = , = (0 , 1)
( )

10. Parallel lines have the same slope Perpendicular lines have negative reciprocal slopes Lines that have unrelated slopes are neither parallel nor perpendicular

11. hmmm.. How could I use slope to tell if a triangle had a right angle?
For instance, given these vertices of a triangle, how could I tell if it was a right triangle?
(1, 2), (3, 3), (4, 0) -3
1/2
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.
2/-3
guess this is not a right triangle

12. Assignment
* Practice wksht 3.3 A & B
* Wksht pg 194, 6-28