Transcript MY GEOMETRY SCRAP BOOK

JHEUSY DELPOZO
TOGANS
9/17/10
MY GEOMETRY SCRAP
BOOK
TABLE OF CONTENTS
PAGE 1-PARALLEL LINES
PAGE 2-TWO CONGRUENT LINES
PAGE 3-VERTICAL LINES
PAGE 4- PERPENDICULAR LINES
PAGE 5-INTERSECTING LINES
PAGE 6-SUPPLEMENTARY
ANGELSS
 PAGE 7-DIFFERENT
PROPORTIONS






VOCABULARY
PAGE 8-POINT
PAGE 9-LINE
PAGE10-LEGNTH
PAGE11-SEGMENT
PAGE12-RAY
PAGE13-POSTULTE
VOCABULARY
PAGE14-ANGLE
PAGE15-PROTRACTOR
PAGE16-ACUTE
PAGE17-OBTUSE
PAGE18-RIGHT
PAGE19-STRAIGHT
PAGE20-BISECTOR
VOCABURLAY
 PAGE21-COMPLEMENTARY ANGELS
 PAGE22-SEGMENT ADDITION POSTULATE
 PAGE23-ANGLE ADDITION
 PAGE24-DISTANCE FORMULA
 PAGE25-MIDPOINT FORMULA
 PAGE26-IRRATIONAL NUMBER
Parallel lines
 Parallel Lines are
lines that never
intersect. Two
non-vertical
lines are parallel
if and only if
they have the
same slope.
 PAGE 1
Two congruent objects
 TWO CONGRUENT
OBJECTS-two figures are
congruent if they have the
same shape and size. More
formally, two sets of points
are called congruent if, and
only if, one can be
transformed into the other
by an isometry, i.e., a
combination of
translations, rotations and
reflections.
PAGE2
Vertical angels
 Vertical Angles are the angles opposite each other
when two lines cross
 They are called "Vertical" because they share the same
Vertex. (or corner point)
 PAGE3
PERPENDICUALAR LINES
Two lines are perpendicular if the product of their
slopes is -1. Also, the two intersecting lines form
right angles. In a coordinate plane, perpendicular
lines have opposite reciprocal slopes.
 Page 4
INTERSECTING LINES
 INTERSECTING LINES-
Lines that intersect
in a point are called
intersecting lines.
Lines that do not
intersect are called
parallel lines in the
plane, and either
parallel or skew lines
in three-dimensional
space.
 PAGE 5
SUPPLYEMENTARY ANGELS
 SUPPLYEMENTARY
ANGELS-These two
angles (140° and
40°) are
Supplementary
Angles, because
they add up to 180°.
Notice that
together they make
a straight angle.
 PAGE 6
DIFFERENT PROPORTIONS
 Harmonic relation
between parts, or
between different
things of the same
kind; symmetrical
arrangement or
adjustment;
symmetry; as, to be
out of proportion.
 PAGE 7
POINTS
 In geometry, topology and
related branches of
mathematics a spatial point is
a primitive notion upon which
other concepts may be
defined. In geometry, points
have neither volume, area,
length, nor any other higher
dimensional analogue. Thus, a
point is a 0-dimensional
object. In branches of
mathematics dealing with set
theory, an element is often
referred to as a point.
 PAGE 8
LINE
 In Euclidean geometry,
a line is a straight
curve. When geometry
is used to model the
real world, lines are
used to represent
straight objects with
negligible width and
height.
 PAGE 9
LENGTH
 Geometric
measurements, length
most commonly refers
to the longest
dimension of an object.
In certain contexts, the
term "length" is
reserved for a certain
dimension.
 Page 10
Segment
 A line has no
endpoints, therefore
you cannot measure
how long it is.A line
segment however, has
2 endpoints and the
length of a line
segment can be
measured.
 Page 11
RAY
 A ray is a part of a
line that begins at
a particular point
(called the
endpoint) and
extends endlessly
in one direction. A
ray is also called
half-line.
 PAGE 12
POSTULATE
 The Basic Postulates
& Theorems of
Geometry. These are
the basics when it
comes to postulates
and theorems in
Geometry. These are
the ones that you
have to know.
 PAGE 13
ANGLE
 In geometry, an angle is the
figure formed by two rays
sharing a common
endpoint, called the vertex
of the angle.[1] The
magnitude of the angle is
the "amount of rotation"
that separates the two rays,
and can be measured by
considering the length of
circular arc swept out when
one ray is rotated about the
vertex to coincide with the
other (see "Measuring
angles", below).
 PAGE 14
PROTRACOR
 In geometry, a
protractor is a
circular or
semicircular tool for
measuring an angle
or a circle. The units
of measurement
utilized are usually
degrees.
 PAGE 15
ACUTE
 In geometry, an angle is the
figure formed by two rays
sharing a common
endpoint, called the vertex
of the angle.[1] The
magnitude of the angle is
the "amount of rotation"
that separates the two rays,
and can be measured by
considering the length of
circular arc swept out when
one ray is rotated about the
vertex to coincide with the
other (see "Measuring
angles", below)
 PAGE 16
OBTUSE
 slow to understand: slow to
understand or perceive
something
 - between 90º and 180º:
describes an angle greater
than 90º and less than 180º
 - with internal angle greater
than 90º: describes a
triangle with one internal
angle greater than 90º
 PAGE 17
RIGHT
 In geometry we
frequently refer to
what are called
reference right
triangles. These are
right triangles whose
angles measure 30-6090 degrees, and also
45-45-90 degrees.
 PAGE 18
STRAIGHT
 In Euclidean geometry,
a line is a straight
curve. When geometry
is used to model the
real world, lines are
used to represent
straight objects with
negligible width and
height.
 PAGE 19
BISECTOR
 In geometry, bisection is the
division of something into two
equal or congruent parts,
usually by a line, which is then
called a bisector. The most
often considered types of
bisectors are the segment
bisector (a line that passes
through the midpoint of a
given segment) and the angle
bisector (a line that passes
through the apex of an angle,
that divides it into two equal
angles).
 PAGE 20
COMPLEMENTARY ANGLES
 These two angles (40°
and 50°) are
Complementary
Angles, because they
add up to 90°. Notice
that together they
make a right angle.
 PAGE 21
SEGMENT ADDITION POSTULATE
 In geometry, the
segment addition
postulate states that if
B is between A and C,
then AB + BC = AC. The
converse is also the
same. If AB + BC = AC,
then B is between A
and C.
 PAGE 22
ANGLE ADDITION
 If the sum of the two angles
measure up to 90°, then the
angles are called to be
‘complementary angles’.
 If the sum of the two angles
measure up to 180°, then
the angles are called to be
‘supplementary angles’.
 The angles sharing a
common side are called as
‘adjacent angles’.
 PAGE 23
DISTANCE FORMULA
 In analytic
geometry, the
distance between
two points of the
xy-plane can be
found using the
distance formula.
 PAGE 24
MIDPOINT FORMULA
 Demonstrates
how to use the
Midpoint
Formula, and
shows typical
homework
problems using
the Midpoint
Formula page 25
Irrational NUMBER
 In mathematics, an irrational
number is any real number
which cannot be expressed as
a fraction a/b, where a and b
are integers, with b non-zero,
and is therefore not a rational
number. Informally, this
means that an irrational
number cannot be
represented as a simple
fraction. Irrational numbers
are precisely those real
numbers that cannot be
represented as terminating or
repeating decimals.
 Page 26