Transcript Angle

Applied Geometry
Lesson: 3 – 1
Angles
Objective:
Learn to name and identify parts of an angle.
Ray
What is a ray?
Opposite rays: two rays that are
part of the same line and have only
their endpoints in common.
XY and XZ
Angle
Angle: a figure formed by two noncollinear
rays that have a common endpoint and are
not opposite rays.
Vertex: the common endpoint
Sides: the two rays that make up the angle
Angle…
What if the rays were collinear?
What would the angle look like?
A
B
C
Straight angle: the figure formed by opposite rays.
Naming Angles
More than one way to name:
 Name
by letters (follow the lines)
 Vertex
 Name
is always middle letter
by vertex
 *Warning*
 Name
Only use if there is one angle
by number (only if given)
Name the angle in all
ways
DEF
FED
E
2
Example
Name the angle in four ways. Then
identify its vertex and its sides.
ABC
Vertex: B
CBA
Sides:
B
1
BA, BC
Name the whole angle in as
many ways as possible
MPO
OPM
Cannot use vertex to name because there are 3 angles with
vertex P not one.
Cannot use number to name because there is not a number that
represents the whole angle.
Name all angles having
W as their vertex.
XWZ
3 (or XWY )
4 (or ZWY )
Do not name the same angle twice.
Not asking for the different ways to name, just asking for angles.
Name all angles having
W as their vertex.
AWC
1
2
Name all angles having
W as their vertex.
UWR 5
UWS 4
TWR 3
Parts of an angle
An angle separates a plane into three
parts
 Interior
of the angle
 Exterior of the angle
 On the angle itself
Tell whether each point is in the
interior, exterior, or on the angle.
Interior
On
Exterior
Homework
Pg. 92 1 – 8 all, 10 – 32 E