Lesson 1.6b: Identifying Angle Pairs
Lesson 1.8: The Coordinate Plane
“Reason is powerless in the expression of love.”
-Damien Hirst
Angle Pairs
Vertical Angles: Two angles whose sides are opposite rays
1
3
4
2
What are the pairs of vertical angles in the diagram?
Angle Pairs
Adjacent Angles: Two coplanar angles with a common side, a
common vertex, and no common interior points
1
2
3 4
Angle Pairs
Complementary Angles: Two angles whose measures have sum of
90°
76°
1
2
<1 + <2 = 90°
14°
76° + 14°= 90°
Angle Pairs
Supplementary Angles: Two angles whose measures have sum of
180°
1
2
<1 + <2 = 180°
131°
49°
131° + 49°= 180°
Making Conclusions from a Diagram
1
5
Which angles are…
Adjacent?
Supplementary?
Vertical?
4
3
2
Making Conclusions from a Diagram
2
1
3
4
5
If m1 is 62°, find the measure of the remaining angles.
Making Conclusions from a Diagram
B
A
(10x+5)°
(15x-20)°
C
O
Using the figure above, find mAOB, mBOC, and mAOC.


The Coordinate Plane
Finding the Distance (using Pythagorean Theorem)
The Distance Formula
The Distance Formula: The distance d between two points A(x1, y1)
and B(x2, y2) is
d  ( x2  x1 )  ( y2  y1 )
2
2
Example: Find the distance between (5, 2) and (-4, -1).
The Distance Formula
Each morning Juanita takes the “Blue Line” subway from
Oak Station to Jackson Station. Find the distance Juanita
travels between Oak Station and Jackson Station.
The Midpoint Formula
The Midpoint Formula: The coordinates of the midpoint M of AB
with endpoints A (x1, y1) and B (x2, y2) are the following:
x1  x 2 y1  y 2 
M  
,

 2
2 
Example: Find the midpoint between (-3, 5) and (7, -3).

The Midpoint Formula – In Groups!
Find the endpoint B of AB if the midpoint is (3,4) and A is (-3, -2).
Lesson 1.6b: Identifying Angle Pairs
Lesson 1.8: The Coordinate Plane
HW: p.40 #15-23, 33, 34
p.56 #1-9 odd, 18, 20, 24, 30
Tools: Distance formula, midpoint formula
“Reason is powerless in the expression of love.”
-Damien Hirst