Download Geometry Chapter 1

Geometry Chapter 1
Section Term
1.1 Point
(pt)
1.1
Line
1.1
Collinear
(1.1)
Plane
(pl.)
(1.1)
1.1
1.1
1.1
Coplanar
(1.1)
Space
(1.1)
1.2
Line Segment
(seg)
1.2
Measure of a
Segment
Definition
A location. It is drawn as a dot, and
named with a capital letter. It has no
shape or size. “undefined term”
A line is made up of points and has no
thickness or width. It goes no forever
(represented by arrows). You can
name a line with ONLY TWO points on
the line (with a line symbol above it) or
with a lowercase script letter. **There
is exactly one line through any two
points. “undefined term”
Points that are on the same line are
collinear.
A flat surface made up of points. A
plane has no depth, only length and
width. It is drawn as a shaded foursided figure and named by any three
non-collinear points or a uppercase
script letter. “undefined term”
**Through any three non-collinear
points is exactly one plane.
Points that exist on the same plane are
coplanar.
Space is a boundless, three dimensional
set of all points. Space can contain
lines and planes. In space, lines
intersect at one point, and planes
intersect at one line.
A line segment is part of a line with a
beginning and end. The points that
create the beginning and end are called
endpoints. You name a segment by
its endpoints and a segment symbol
above them.
Can be written in two ways:
1. the endpoint letter with no
symbol – “the distance from
point __ to point __”
2. a lowercase m in front of the
name of the line segment with
the segment symbol above it “the measure of segment ___”
Name ______________________
1.2
Precision
Precision of any measurement depends
on the smallest unit available. Your
precision will be half of the smallest unit
available.
To find smallest unit, think of the
increments you are counting or
measuring by. (i.e. 48cm to 49cm to
50cm has a smallest increment of 1 cm,
so the precision is 0.5 cm)
1.2
Betweenness
A point is between two other points if
you can add the smaller segments
created with the point and it equals the
bigger segment. “If M is between A and
B, then AM + MB = AB”
of points
1.2
Congruent
Segments

1.3
segs 
Distance
If two segments are equal in measure,
then they are congruent.
If two segments are congruent, then
they are equal in measure.
If  , then =.
The distance between two points is the
length of the segment connecting them
and can be found with the distance
formula: The distance between points
Find CD if C(2, 6)
and D(-1, 3).
 x1 , y1  and  x2 , y2 
can be found by:
 x2  x1    y2  y1 
2
1.3
Midpoint
(mp)
If =, then  .
2
A midpoint of a segment is the point
halfway between the endpoints of a
segment.
If a point is a midpoint, then it divides
the segment into two equal segments.
If a point divides a segment into two
equal segments, then it is the midpoint.
The mp between points
 x1 , y1  and  x2 , y2 
 x1  x2 y1  y2 
,


2 
 2
can be found by
Find the mp of CD
if C(-1,2) and
D(5, 3).
1.3
Segment
Bisector
(seg bis)
1.4
Degree
1.4
Ray
1.4
Opposite
Rays
1.4
Angle
1.4
Right Angle
1.4
Acute Angle
1.4
Obtuse Angle
  or 
Straight
Angle
Any segment, line, or plane that
intersects a segment at its midpoint is
called a segment bisector.
If segment is bisected, then it’s divided
into two equal segments.
If a segment is divided into two equal
segments, then it is bisected.
Unit of rotation around a circle. A unit
for measuring angles.
Symbol:
A ray is part of a line. It has one
endpoint and extends infinitely in one
direction. Rays are named using the
endpoint first (always) and one other
point on the ray. You can only use the
two letters and the ray symbol above it.
If you choose a point on a line, that
point determines exactly two rays called
opposite rays. Looks like a “straight
line”
An angle is formed by two rays that
have a common endpoint. The rays are
called the sides of the angle, and the
common endpoint is called the vertex
of the angle.
If an angle measures 90 degrees, then
it is a right angle.
If an angle is a right angle, then it
measures 90 degrees.
If an angle measures between 0 and 90
degrees, then it is an acute angle.
If an angle is an acute angle, then it
measures between 0 and 90 degrees.
If an angle measures between 90 and
180 degrees, then it is an obtuse angle.
If an angle is an obtuse angle, then it
measures between 90 and 180 degrees.
If an angle measures 180 degrees, then
it is a straight angle.
If an angle is a straight angle, then it
1.4
Congruent
Angles

1.4
s
Angle
Bisector
measures 180 degrees.
A straight angle looks like a straight
line, but since we are looking at it in
terms of rotation, it measures 180
degrees, it can be both an angle and a
straight line.
If two angles are equal in measure,
then they are congruent.
If two angles are congruent, then they
are equal in measure.
If a ray divides an angle into two
congruent angles, then it is an angle
bisector.
If ray bisects an angle, then it divides it
into two congruent angles.
If =, then  .
If  , then =.
1.5
Adjacent
Angles
Two angles that lie in the same plane,
have a common vertex, common sides,
BUT do NOT overlap.
1.5
Vertical
Angles
Two non-adjacent angles formed by two
intersecting lines.
1.5
Linear Pair
Pair of adjacent angles whose noncommon sides are opposite rays.
1.5
Complementar
y Angles
If two angles are complementary, then
they add up to 90 degrees.
If two angles add up to 90 degrees,
then they are complementary.
**They do not have to be adjacent to
be complementary, but if they are
adjacent they will form a right angle.
If two angles are supplementary, then
they add up to 180 degrees.
If two angles add up to 180 degrees,
then they are supplementary.
**They do not have to be adjacent to
be supplementary, but if they are
adjacent they will form a straight angle
and be a linear pair.
If two lines are perpendicular, then they
intersect to form 90 degree angles
If two lines intersect to form 90 degree
angles, then they are perpendicular.
Comp
1.5
 s
Supplementary
Angles
Supp 
1.5
s
Perpendicular
lines
 
1.5
Assumptions
Be careful with diagrams, just because something looks like it is true does not
mean that it is true.
What you can assume from a diagram:
1. Adjacent angles
2. Linear pairs
3. Supplementary angles
CANNOT ASSUME:
1. Right Angles
2. Perpendicular or parallel lines
Congruent segments or angles
1.6
Polygons
A closed figure whose sides are all
segments that only intersect one other
side at each endpoint.
It is named by all of the endpoints
(vertices) in consecutive order.
1.6
Concave
Polygon
1.6
Convex
Polygon
It is a polygon with at least one angle
that is greater than 180 degrees. It
looks dented or caved in.
It is a polygon with all angles
measuring less than 180 degrees.
1.6
Classifying
Polygons
A polygon can be classified by the number of sides that it has. A polygon with n
number of sides is called a n-gon.
Number of Polygon name
sides (n)
3
4
5
6
7
8
9
10
11
12
15
n
1.6
Regular
Polygon
A polygon that is equilateral (all sides
are equal) and equiangular (all angles
are equal).
1.6
Perimeter
The perimeter of a polygon is the sum
of the lengths of its sides.
**To find the perimeter of a figure
when given coordinates, requires you to
use the distance formula for each side,
then add those lengths (distances).