Download 1-4 = Angles - David Michael Burrow

Angle
• Two rays with the same
endpoint
•
The rays are the sides
of the angle.
•
The common endpoint
of the 2 rays is the
vertex of the angle.
Name the sides and vertex of
this angle:
Name the sides and vertex of
this angle:
We sometimes refer to the
interior and exterior of an
angle.
What points lie
 on the interior?
 on the exterior?
 on the
angle?
You can name angles many
different ways:
•
named with 1 letter, the letter
must be the vertex
•
named with 3 letters, the
middle letter is the vertex, and
the others are 1 point on each
ray
Give as many names as you
can for these angles.
Give as many names as you
can for these angles.
DEF
FED
E
Give as many names as you
can for these angles.
TUV
VUT
U
We sometimes also name
angles with numbers,
particularly when there are
several angles in the same
picture.
5 is at
the bottom
left.
The measure of an angle
refers to how wide the angle
opens, NOT how long the
sides are (because they go on
forever) or which way it points.
There are
many ways
to measure angles.
The oldest and most common
unit of measurement is the
degree.
•
A full circle has 360o
•
A straight line has
o
180
Types of Angles
•
Acute
• less than 90o
•
Right
• exactly 90o
• We often use a box to
show an angle is a
right angle.
•
Obtuse
• between 90o and 180o
•
Straight
• exactly 180o
• same as a line
The tool used to measure
angles is called a protractor.
The tool used to measure
angles is called a protractor.
Various types of protractors
have been used for thousands
of years, mostly in navigation
and construction.
In modern practical applications,
angles are measured by sighting
laser beams.
We refer to the measure of an
angle with notation that uses
the letter “m”.
mACD = 138
mB = 80
IMPORTANT:
We don’t normally
use protractors much in
geometry. This is because
pictures are intended to give the
idea of what’s going on, but they
may not necessarily be accurate.
Congruent Angles
Angles are congruent if and only
if they have the same measure.
R  Q
Congruent Angles
In drawings we show angles
are congruent by marking the
same arcs of a circle inside
the angles.
Find mCAB.
64 – 53 = 11o
Find mCAB.
mADC = 50
Find x
Find m BDC
mADC = 50
Find x
Find m BDC
x + 7 + 2x + 19 = 50
3x + 26 = 50
mADC = 50
Find x
Find m BDC
3x + 26 = 50
3x = 24

x=8
mADC = 50
Find x
Find m BDC
m BDC = 2x + 19
2  8 + 19 = 16 + 19 = 35o
Remember …
 Angle, side vertex, interior,
exterior
 Naming angles
 Measuring angles,
protractor, degree
 Acute, obtuse, right, straight
 Congruent angles