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Transcript 
Advanced Geometry
Inductive Reasoning
Lesson 2
Angles
Rays
Drawn as: a line with one endpoint and one
arrowhead
N
D
Named by: 2 points and a ray symbol
 the endpoint must be named first
ND
 the arrow always points to the right
Opposite rays are two collinear rays that point in
opposite directions.
Angle
Parts of an Angle
vertex – the common endpoint B
sides – the rays BA and BC
Regions
interior
exterior
on the angle
Naming an Angle
Use an angle symbol and…
- the number inside the angle.
- three points with the vertex
in the middle.
- the vertex point.
*You can only
use this method
if there is ONE
angle at the
vertex.
Examples:
Name the sides of
5.
BG and BE
Write another name for 6.
EBD, DBE ,
FBD, OR DBF
Name all angles that have B as
a vertex.
Angle Classifications
• Right angle – measures exactly 90°
• Acute angle – measure is less than 90°
• Obtuse angle – measure is greater
than 90° and less than 180°
• Straight angle – an angle with a
degree measure of exactly 180°
(a.k.a. straight line)
Angle Bisector
PQ
bisects
RPS
RPQ  QPS
Examples: In the figure, QP and QR are opposite rays, and
QT bisects RQS .
If mRQT  6 x  5, and mSQT  7 x  2,
find mRQT .
Angle Relationships
Adjacent Angles
Adjacent angles are beside
each other.
They share a vertex and side.
They do not overlap.
Vertical Angles
Vertical angles are NOT
adjacent.
They share a vertex only.
Vertical angles are
congruent.
Linear Pair
Angles of a linear pair ARE
adjacent.
They share a vertex
and a side.
Remember: If two rays are
opposite rays, they create a
straight line.
Example: Name an angle pair that satisfies each condition.
two angles that form a linear pair
VZX and XZW
two acute vertical angles
Complementary Angles
two angles
sum of 90
Supplementary Angles
two angles
sum of 180
LINEAR PAIRS ARE
ALWAYS
SUPPLEMENTARY.
Example:
If BCE and  ECD are
supplementary, find m ECF
and m FCD.
Example:
Find the measures of two supplementary angles if the
difference in the measures of the two angles is 32.
106 and 74
The complement of an angle is 3.5 times smaller than
the supplement of the angle. Find the measure of the
angle.
Perpendicular Lines
Symbol:
a

m1  90
m2  90
m3  90
m4  90
b
a b
Example: Find x so that KO  HM .
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