Week 2 Notes

1
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.

2
1.4 Angles and Their Measures (2 days)
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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
4
If two angles are congruent, their measures are
equal. If the measure of two angles are equal,
they are congruent
D
R
1
2
U
E
C
X
5
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.
6
Acute Angle is between 0 and 90 degrees
Right Angle is exactly 90 degrees
Obtuse Angle is between 90 and 180 degrees
90
Straight Angle is 180 degrees
0
180
7

• 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

8
Adjacent angles, share common side and vertex,
but share NO interior points.
9
C
O
B
A
10
Find the measure of the unknown angles, state if
they are acute, right, or obtuse.
1
76o
11
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.
12

• 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

13
1.5 Segment and Angle Bisectors (2 days)
14
D
B
A
C
E
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.
15
What coordinate is in the MIDDLE of these two
points?
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Find the midpoint.
(5, -2) (3, 6)
(-2, -1) (2, 5)
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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)
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ANGLE BISECTOR is a ray that divides an angle
into two adjacent angles that are congruent.
19
(No Transcript)
20
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
21
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.