Download 8.1 lines and angles

8.1 LINES AND ANGLES
Geometry Definitions:
(opt) POINT: a location in space having no length, width
or depth. We write a dot next to the letter representing
P
that point.
“point P”

(opt) LINE: a straight row of points that goes on forever
in two directions. We draw ARROWs on each end to show
it never ends. We can use any two points identified by
letters on the line to identify it.
“line AB” or
AB AC
A
B
(opt) LINE SEGMENT: a part of a line that has TWO
ENDpoints. It has an uncountable number of points, but it
does NOT go on forever. We name a line segment by
writing the letter corresponding to the points at the ends.
“line segment PR” or
PR
P
Q
R
(opt) RAY: a part of a line having only ONE ENDpoint,
and it goes on forever in the other direction. We always
say or write the ENDPOINT FIRST, regardless of the
orientation of the ray.
“ray CD” or
CD
D
C
PLANE: flat surface having only two dimensions, no
depth.
On a plane two LINES can be INTERSECTING or
PARALLEL:
PARALLEL LINES never cross each other
INTERSECTING LINES cross each other in exactly one
point (if they intersect at right angles they are
“PERPENDICULAR LINES”)
INTERSECTING OR PARALLEL?
NOTE: if it is not STATED that two lines are parallel, you
cannot ASSUME it to be so.
ANGLE: a geometrical figure made of two rays whose
endpoints share a common point called a VERTEX. We
name an angle by using a point from each ray (besides the
endpoint) and placing the point used for the VERTEX in
the MIDDLE. It is easiest to start on one point on a ray,
read the vertex (shared endpoint) and then another point
on the other ray. We can also name the angle just based
on the vertex, as long as it is not shared, or by a number
marking the angle:
Y
“angle XYZ”  XYZ
1
 ZYX
X
Z
 Y
“angle 1”
 1
EX: name the indicated angle
A
B
C
1
3
D
2
4
E
Angles can be MEASURED in DEGREES 
360 
180 
90 
What would a 45  angle look like?
A 15  angle?
Angles have special names depending on how they can be
classified according to their angle measure:
ACUTE angles have measures between 0  and 90 
RIGHT angles measure exactly 90 
OBTUSE angles have measures between 90  and 180 
STRAIGHT angles measure exactly 180 
We will not work with angles measuring over 180 .
Classify each angle as acute, right, obtuse or straight:
As we stated earlier, PERPENDICULAR lines are a kind
of INTERSECTING lines that cross at 90  or “right”
angles. We can identify them by the right angle symbol, or
if the angle is given to measure 90 degrees.
“line
is perpendicular to line
“
W
X
Y
U
Can you name a right angle?
Z
How many are there?
COMPLEMENTARY ANGLES: TWO angles whose
SUM is 90 
23 
67 
SUPPLEMENTARY ANGLES: TWO angles whose SUM
is 180  (“supple gymnast”)
135 
45 
The “fun” begins when we know two angles are
complementary or supplementary, but do not know the
measure of one of them.
Ex: Find the measure of an angle whose COMPLEMENT
is 78
Ex: Find the measure of an angle whose SUPPLEMENT
is 19