Angles and lines
CONTENTS
目录
01
角的分类
02
角的度量
03
角平分线
04
余角和补角
Chapter one
The catalogue of angles
The catalogue of angles
锐角
acute angle
直角
right angle
钝角
obtuse angle
平角
straight angle
优角/反角
reflex angle
周角
round angle
Chapter two
The measurement of angles
degree, minutes,seconds
Degree,
Minutes,Seconds
1°=60'
1'=60''
Degree
Minute
Second
In a complete
Each degree is split
Each minute is split
circle there are
up into 60 parts,
up into 60 parts,
three hundred
each part being
each part being
1/60 of a degree.
1/60 of a minute.
These parts are
These parts are
called minutes.
called seconds.
and sixty degrees.
each part being
one degree.
Decimal
Degree,
number
minutes,
degree
seconds
EX:35.75°=35°+
0.75°×60=35°45'
Exercise:
1.(a) Convert 50°6'21'' to a decimal in
degrees.
(b) Convert 21.256° to D°M'S'' form.
2.Calculation
(1). 54°28'36''+26°50'28''
(2). 180°-76°46'23''
(3). 15°32'20''×5
(4). 54°20'÷6
Chapter
three
Angle bisector
What is an angle bisector?
A line that splits an angle into
two equal angles.
Angle Bisector Theorem
If a point is on the bisector of an
angle, then the point is equidistant
from the sides of the angle
Angle Bisector Theorem Converse
If a point is in the interior of an angle
and equidistant from the sides,
then it lies on the bisector of that
angle.
Chapter four
Complementary angle
Supplementary angle
Complementary angle
Two angles are Complementary when they
add up to 90 degrees.
Supplementary angle
Two Angles are Supplementary when they add up to 180
degrees.
The Propoties of complementary
angle/supplementary angle
There are two types of complementary angles,
adjacent and non-adjacent.
 Adjacent: the angles share a common  Non-Adjacent: the angles do not share
a common side.
side and vertex and are "side-by-side".
Chapter five
Direction and bearing
Direction and Bearing
Direction
The direction to a point
is stated as the number
of degrees east or west
of north or south
the direction of A from O is N30ºE.
Bearing
A bearing is an angle,
measured clockwise
from the north direction.
The bearing of P from O is 065º.
The bearing of Q from O is 300º.