Download Chapter Four Geometry

Chapter 4
Geometry: Lines & Angles
Point
A location in space
Line
a straight path of points
that goes on endlessly
in both directions
Line Segment
a part of a line having
two endpoints
Plane
a flat surface that goes
on endlessly in all
directions
Ordered Pairs
are two numbers that
locate a point on a
coordinate graph. The
first is the X-axis
(horizontal) the second,
is the Y-axis (vertical)
Coordinate
Plane
coordinate planes have
four quadrants that
show positive and
negative axis
Rays & Angles
A RAY is a part of a line that goes on endlessly in one
direction
An ANGLE is formed when 2 rays share the same
endpoint. The shared endpoint is called a VERTEX!
Naming
Angles
* To name an angle, the
vertex can be used alone, OR
you can use the three points
with the vertex in the middle.
* The angles above can be
called <A, <CAB, <BAC and
<D, <EDF, <FDE
Types of Angles
Acute: cutie, less than 90 degrees
Right: straight and strong, exactly 90 degrees
Obtuse: big papa, greater than 90 degrees
Straight: stretches out, exactly straight at 180 degrees
Reflex: flexible angle, overextends more than 180 degrees
Full Rotation: twirl, exactly 360 degrees
Protractor
* You use a protractor to
measure angles. The
VERTEX lines up with the
center point on the bottom.
The bottom ray lines up
with the bottom of the
compass line. The
extending ray, tells you the
measure of the angle in
degrees. READ THE
BOTTOM NUMBER if the
angle is facing right, READ
THE TOP NUMBER if the
angle is facing left!
Straight Angles
Remember that Straight Angles ALWAYS equal 180 degrees.
So if you know one angle, you can subtract it from 180
degrees to figure out the size of the other angle. Look at the
example below.
<AXC + <BXC = 180
62 + n = 180
180 - 62 = 118
So, <AXC = 118 degrees
Measuring Angles
Using a protractor, measure angles, remembering that
angles facing right, use the bottom set of numbers. If
the the angle is facing left, use the top set of numbers.
Parallel Lines
lines that run beside
one another and will
never cross
Perpendicular
Lines
lines that intersect at
exact right angles
Intersecting
Lines
lines that will cross one
another at various angle
measurements
Triangles
A triangle can be classified by the measure of its
angles.
The sum of the measures of the angles of any triangle
equals 180 degrees.
Acute
Triangle
a triangle whose angles
are all less than 90
degrees
Right Triangle
a triangle with one
angle that is exactly 90
degrees
Obtuse
Triangle
a triangle that has one
angle that is over 90
degrees
Remember!!!!
ALL angles of a triangle (when added together) equal
180 degrees. EVERY TIME! No matter what kind of a
triangle, or no matter what the size of the angles … the
sum of the three angles together WILL BE 180 degrees
guaranteed!
Circles
Radius
a line segment from the
center point to any point
on the circle, a radius is
1/2 of a diameter, and is
labeled as a line segment
Chord
a line segment that
connects any two
points on a circle, it is
labeled like a segment
Diameter
a chord that passes
through the center point,
cutting the circle in half
(180 degrees), it too is
labeled as a segment
Central Angle
an angle with its vertex
in the center of the
circle, labeled like a
normal angle
Measuring
Angles in a
Circle
You can measure a lot of angles in a circle
simply by remembering a few things!
1. a diameter = straight angle = 180
degrees
2. right angles are 90 degrees
3. 1/2 of right angles are 45 degrees
4. the whole circle is 360 degrees
5. you can use subtraction to find the
difference of the angles that are left