Download Week 2 Notes

Week 2 Notes
• Note, not all slides are here, some you will
have to write in other space like paper, but
this should help minimize some writing.
You figure out your own method.
1.4 – Angles and Their
Measures (2 days)
Angles
L
A
E
N
1
G
S
Angles are formed by two rays with the same initial
point.
Two rays are called the sides.
The initial endpoint is called the vertex
Definition of congruent angles
m1  m2
1  2
If two angles are congruent, their measures are equal.
If the measure of two angles are equal, they are
congruent
D
U
1
R
E
C
2
X
Protractor Postulate
A
O
B
Consider a point A on one side of OB. The rays of the form OA
can be matched one to one with the real numbers from 0 to 180.
The measure of AOB is equal to the absolute value of the
difference between the real numbers for OA and OB.
Acute – Angle is between 0 and 90 degrees
Right – Angle is exactly 90 degrees
Obtuse – Angle is between 90 and
180 degrees
90
180
20
0
180
Straight – Angle is 180 degrees
90
120
A point is in the interior of an angle if it is
between points that lie on each side of the
angle.
A points is in the exterior of an angle if it is not
on the angle or its interior
D
U
C
BUC and CUD
are adjacent.
BUC and BUD
B
U
C
are not adjacent.
D
Adjacent angles, share
common side and
vertex, but share NO
interior points.
T
R
O
Y
Angle Addition Postulate
If B is in the interior of
AOC, then
mAOB  mBOC  mAOC
C
O
B
A
Find x
Find the measure of the unknown angles, state if they are
acute, right, or obtuse.
B
D
A 1
4
C
2
3
E
F
1
76o
Draw angle ABC that is 90o. Draw right angle DBF so
that angle ABF and DBA is 45o and A is in the interior of
angle DBF and F is in the interior of angle ABC.
Find
mDBA 
mDBC 
mFBC 
• Draw a right angle KIM. Draw angle JIQ
such that M is in the interior of angle JIQ
and Q is in the interior of KIM and JIM is
30 degrees and MIQ is 60 degrees
1.5 – Segment and Angle
Bisectors (2 days)
D
A
E
B
C
DE , DE , BE ,etc
are segment
bise ctors
SEGMENT BISECTOR – A line, segment, or ray
that INTERSECTS THE SEGMENT AT THE
MIDPOINT!
The MIDPOINT of a segment divides the
segment into TWO congruent parts.
Definition of midpoin t : AB  BC
AB  BC
B is midpoin t of AC
What coordinate is in the MIDDLE
of these two points?
MIDPOINT FORMULA
 x1  x2 y1  y2 
( xm , y m )  
,

2 
 2
Find the midpoint.
MIDPOINT FORMULA
 x1  x2 y1  y2 
( xm , y m )  
,

2 
 2
(-2, -1) (2, 5)
(5, -2) (3, 6)
Given an endpoint and the midpoint, find the other
endpoint. A is an endpoint, M is a midpoint
A (5, -2) M (3, 6) B (x, y)
A (2, 6) M (-1, 4) B (x, y)
B
T
20
20
A
R
ANGLE BISECTOR – is a ray that divides an
angle into two adjacent angles that are
congruent.
Definition of angle bisector
mBTA  mATR
BTA  ATR
TA bisects BTR
BD bisects ABC, find x
A
A
x5
D
D
B
C
1
x  10
2
x2  4
7x  6
B
C
Constructing a perpendicular bisector.
1) Point on one end, arc up and down.
2) Switch ends and do the same
3) Draw line through intersection
Bisect an angle
1) Draw an arc going across both sides of the angle.
2) Put point on one intersection, pencil on other, draw an arc
so that it goes past at least the middle.
3) Flip it around and to the same.
4) Line from vertex to intersection.