APM Welcome, APM North West Network Conference, Synergies Across Sectors
1 directed angle
1. REDSEA STEM HIGH SCHOOL
MA1.01 DIRECTED ANGLE
2019-2020
MR George Alfy Shaker
01119135313
George.Alfy@stemredsea.moe.edu.eg
2.
3. Angle is :
• Angle is union of two rays with
a common start point.
• The common point is called
«Vertex» of the angle and the
two rays are called "sides“ of
the angle.
4. i.e.: In the figure opposite:
• The Vertex of the angle is B
and the two sides of the angle
are BA & BC .
• BA ∪ B C = (ABC)
and is written as ABC or
CBA or B .
5. Degree Measure System
degree measure depends on dividing the circle
into 360 equal arcs in length, then:
1- The central angle subtends one of these arcs, its
measure equals one degree (1o)
2- Each degree is subdivided into 60 equal
divisions , each division is called a minute and is
denoted by (1')
3- Each minute is subdivided into 60 equal
divisions, each division is called " a second" and is
denoted by (1'')
i.e.: 1c = 60' and 1' = 60''
6. Directed Angle
We shall now put a further
emphasis on the order of the
two rays forming the angle,
then it is written in the form
of an ordered pair (OA , OB)
OA is the initial side and OB is the terminal
side of the angle of vertex O as in figure (1) .
7. If the initial side is OB and
the terminal side is OA , then
it is written as ( OB , OA ) in
figure (2).
8. The directed angle
AOB = ( OA , OB )
The directed angle
BOA = ( OB , OA )
9. Question
Is ( OA , OB ) = ( OB , OA ) ?
Is AOB = BOA ?
Is the directed angle AOB = the directed
angle BOA ?
10. Standard position of the
directed angle
An directed angle is in the standard position if it
satisfies the next two conditions :
1) Its vertex is the origin of rectangular coordinate
system.
2) Its initial side lies on the positive direction of
the x-axis.
11. Is the directed angle AOB in the standard
position? Explain your answer.
12. Exercise (1) :
Which one of the following ordered pairs
expresses a directed angle in its standard
position?
13. Exercise (2) :
Which of the following directed angles is in the
standard position?
14. Positive and negative measures
of a directed angle
In figure (1):
The directed angle,
resulting from an
anticlockwise rotation
has a positive measure.
15. In figure (2):
The directed angle,
resulting from a
clockwise rotation has
a negative measure.
16. Exercise (3) :
Find the measure of the directed angle in each of
the following figure:
