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Geometry Dictionary

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Transcript of Geometry Dictionary

Geometry Dictionary
We are two angles that share a side and a vertex but never overlap.
What are we?

We are Adjacent Angles!
Angle Bisector!
Angle
An angle measures the amount of turn.
Area
Area is a measure of the size of a 2-dimensional surface.
A shape, formed by two lines or rays diverging from a common point (the vertex)
Acute
refers to an angle less than 90°
Bisects
to divide into two equal parts
circumference
The distance around the edge of a circle.
collinear points
A set of points that lie in a straight line
compass
A compass is a drawing instrument used for drawing circles and arcs.
two angles are said to be complementary when they add up to 90°
complementary
Congruent angles
Equal in size and shape
conjecture
an opinion or conclusion formed on the basis of incomplete information.
Example; Sarah bought ------- apples she then bought _______ pears. So Sarah must have 20 pieces of fruit.
Conjecture.
construction
construction is the act of drawing geometric shapes using only a compass and straightedge. No measuring of lengths or angles is allowed.
congruent segments
Definition: Line segments are congruent if they have the same length
coordinate
Coordinates are a set of values that show an exact position
coplanar
Two objects are coplanar if they both lie in the same plane.
counterexample
An example which disproves a proposition.
definition
distinctness of outline or detail
distance
The distance between two points is the length of a straight line segment that links them.
distance formula
the distance between two points of the xy-plane can be found using the distance formula.
endpoints
either of two points or values that mark the ends of a line segment or interval
exterior
being on an outside surface : situated on the outside
inductive reasoning
Inductive reasoning (as opposed to deductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth
initial point
The first point at which a moving target is located on a plotting board.
interior
lying, occurring, or functioning within the limiting boundaries
intersection
the place or point where two or more things come together
line
linear pair
two angles that are adjacent and supplementary
line segment
A geometrical object that is straight, infinitely long and infinitely thin.
measure
midpoint
A point on a line segment that divides it into two equal parts
The halfway point of a line segment
midpoint formula

Use the midpoint formula to find the midpoint between points (x1, y1) and (x2, y2
obtuse
In math, the word 'obtuse' usually involves an angle greater than 90°.
a long narrow mark on a surface
opposite rays
two rays with a common endpoint that form a line
perimeter
The distance around the edge of a figure or shape. For example it is the sum of the lengths of each side of polygon. For circles and ellipses, it is called the circumference.
plane
A flat surface that is infinitely large and with zero thickness
point
A precise location or place on a plane. Usually represented by a dot.
postulates
Postulate is a true statement, which does not require to be proved.
ray
A portion of a line which starts at a point and goes off in a particular direction to infinity.
an angle that is between 90 and 180 degrees
segment bisector
is a line or a ray or a segment that divides a line segment into two equal parts.
sides
any line segment forming part of the perimeter of a plane geometric figure
straight
A straight angle changes the direction to point the opposite way. It looks like a straight line. It measures 180°
straight edge
An idealized mathematical object having a rigorously straight edge which can be used to draw a line segment.
supplementary angles
Two Angles are Supplementary if they add up to 180 degrees.
undefined terms
These basic terms are used to define or explain more complicated terms or concepts.
vertex
The common endpoint of two or more rays or line segments
vertical angles
each of the pairs of opposite angles made by two intersecting lines.
Expansion of a figure
When you resize a shape it gets bigger or smaller.
... but it still looks similar:
all angles stay the same
relative sizes are the same (for example
the face and body are still in proportion)
Horizontal Stretch
A stretch in which a plane figure is distorted horizontally.
Line of symmetry
If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry.
non-rigid transformation
A non-rigid transformation is a mathematical phenomenon in which the shape of the curve is altered after a transformation has been done.
Parallelogram
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).
RECTANGLE
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral
Reflectional symmetry
Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to recognize, because one half is the exact reflection of the other half.
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
Rigid Motion
translations preserving orientation of a shape
Rigid Transformation
a rigid transformation (isometry) of a vector space preserves distances between every pair of points.
Rotational Symmetry
With Rotational Symmetry, the shape or image can be rotated and it still looks the same.
Sequence of Transformations
In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space).
TRAPEZOID
In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid
VERTICAL STRETCH
A stretch in which a plane figure is distorted vertically.
ascertain the size, amount, or degree of (something) by using an instrument or device marked in standard units or by comparing it with an object of known size.
RIGHT
Hello and my name is Elizabeth Finley, Singers class period 6. This is my 10th grade Geometry Dictionary. It is full of vocabulary terms that I had to learn. Please enjoy and I hope it is informational!
angle measure
The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are sometimes called congruent angles.
The measure of angle O is the quotient of s and r.
angle side angle
"ASA" means "Angle, Side, Angle" This means we are given two angles and a side between the angles.
alternate interior angles
The pairs of angles on opposite sides of the transversal but inside the two lines are called Alternate Interior Angles.
angle angle side
"ASA" means "Angle, Side, Angle" This means we are given two angles and a side between the angles.
alternate exterior angles
The pairs of angles on opposite sides of the transversal but outside the two lines are called Alternate Exterior Angles.
altitude
In the case of a triangle, a common way to calculate its area is 'half base times height' where the 'height' is the altitude, altitude and base of a triangle or the perpendicular distance from the base to the opposite vertex. The base can be any side, not just the one drawn at the bottom.
Angle Angle (AA)
Similarity
In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.
(Note that if two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.)
adjacent
being near or close, esp having a common boundary; adjoining; contiguous
arc functions
Inverse trigonometric functions are also known as arc functions.
Just as there are 6 trigonometric functions, there are also 6 trigonometric arc functions - arc sine, arc cosine, and so on.
auxiliary line
an Auxiliary line segment is also referred to as a angle bisector, it bisects an angle.
archimedes principle
indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. Archimedes of Syracuse formulated this principle, which bears his name.

BETWEENNESS
is a centrality measure of a vertex within a graph
The center of dilation
is a fixed point in the plane about which all points are expanded or contracted.
collinearity
is a property of a set of points, specifically, the property of lying on a single line
contraction
to draw back; to shrink
congruenece
is the state achieved by coming together, the state of agreement.
corresponding sides
If the relative position of two sides is same in two figures, then they are called Corresponding Sides.
cosine
The cosine function is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent).
a trigonometric function whose value for the complement of an angle is equal to the value of a given trigonometric function of the angle itself


Example;
<the sine is the cofunction of the cosine>
Cofuncion
DENSITY
the volumetric mass density, of a substance is its mass per unit volume.
Thank You!
I hope you appreciated the hard work and effort I put into making this an informational yet cute looking presentation.
Dilation
is where the shape grows or shrinks but keeps the same overall shape. It's a little like zooming in or out on a camera.
Corresponding angles
are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection.
face of a polyhedron
If you count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron, you can discover an interesting thing:
The number of faces plus the number of vertices minus the number of edges equals 2
This can be written neatly as a little equation:
F + V - E = 2
geometric mean
In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root (where n is the count of numbers) of the product of the numbers.
the longest side of a right triangle, located opposite the right angle. also hypothenuse. Origin: Classical Latin hypotenusa
hypotenuse image
an object that has no symmetry ... The definition of a irregular polygon is any polygon that is not a regular polygon. ...
irregular object
side side side
side angle side

these are both congruency statements
weight density
the weight per unit volume of a substance or object.
trigonometric ratios
are special measurements of a right triangle (a triangle with one angle measuring 90o).

tangent

line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
A
scale factor
is a number which scales, or multiplies, some quantity. In the equation y=Cx, C is the scale factor for x.
is used either to refer to a geometric similarity, or to a matrix transformation that results in a similarity.
Similarity transformation
Solution of triangles is the historical term for solving the main trigonometric problem of finding the characteristics of the triangle when some, but not all, of these characteristics are given.
Solve a triangle
is one of the four fundamental states of matter (the others being liquid, gas, and plasma). It is characterized by structural rigidity and resistance to changes ...
SOLID
Similarity
likeness: the possession of one or more qualities or features in common
shared characteristic: a quality or feature that two or more people or things have in common
similar
alike: sharing some qualities, but not identical
with same shape or angles: describes geometric figures
that differ in size or proportion but not in shape or angular measurements
identical: exactly the same
sine
In mathematics, the sine function is a trigonometric function of an angle. The sine of an angle is defined in the context of a right triangle.
ratio
In mathematics, a ratio is a relationship between two numbers of the same kind e.g., objects, persons, students, spoonfuls, units of whatever identical dimension
Pythagorean theorem
In mathematics, the Pythagorean theorem—or Pythagoras' theorem—is a relation in Euclidean geometry among the three sides of a right triangle.
perpendicular bisector
A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint
pre-image
the original figure prior to transformation
proportion
the relationship between different things or parts with respect to comparative size, number, or degree; relative magnitude
opposite
on facing side: positioned so as to face somebody or something from the other side of an intervening space
facing away: pointing, facing, or moving away from each other
totally different: different from or contrary to something or each other in every respect
oblique
Slanting. Not up-down or left-right.

Angles: not 90°, 180°, 270°, etc,
MAPPING
A rule of correspondence established between sets that associates each element of a set with an element in the same or another set.
median
the median is the numerical value separating the higher half of a data sample, a population, or a probability distribution,
mass density
The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is
ρP.
law of sines
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law;

If the events are A and B respectively, this is said to be "the probability of A given B". It is commonly denoted by P(A|B), or sometimes PB(A).
A GIVEN B
association

(of an operation on a set of elements) giving an equivalent expression when elements are grouped without change of order, as ( a + b ) + c = a + ( b + c ).
BASE B
The digits of a number x in base b (for integer b>1) can be obtained in Mathematica using IntegerDigits[x, b].

Let the base b representation of a number x be written

(a_na_(n-1)...a_0.a_(-1)...)_b,
(1)
(e.g., 123.456_(10)). Then, for example, the number 10 is written in various bases as

10 = 1010_2
(2)
= 101_3
(3)
= 22_4
(4)
= 20_5
(5)
= 14_6
(6)
= 13_7
(7)
= 12_8
(8)
= 11_9
(9)
= 10_(10)
(10)
= A_(11),
(11)
since, for example,

10 = 1·2^3+1·2^1
(12)
= 1·3^2+1·3^0
(13)
= 2·4^1+2·4^0,
(14)
and so on.

Common bases are given special names based on the value of b, as summarized in the following table.
categorical variable
In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values.
Cavalieri's Principle
If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.
combination
In mathematics, a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter.
complement
a number or quantity of something required to make a group complete.
complementary events
In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur.
In the world of probability,
compound events
are probabilities of two or more things happening at once.
In probability theory, a
conditional probability
measures the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the events are A and B respectively, this is said to be "the probability of A given B". It is commonly denoted by P(A|B), or sometimes PB(A).
A
convenience sample
is one in which the researcher uses any subjects that are available to participate in the research study.
To name or list (the units of a group or collection) one by one in order to determine a total; number. b. To recite numerals in ascending order up
COUNTING METHODS
CROSS SECTION
In geometry, a cross section is the intersection of a figure in a 2-dimensional space with a line, or of a body in a 3-dimensional space with a plane, etc. When cutting an object into slices, one gets many parallel cross sections.
Dependent events
Events that occur only after a previous event.
dependent variable
A dependent variable is what you measure in the experiment and what is affected during the experiment.
Dissection.
Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other.
ELEMENT
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
For example consider the set B = {1, 2, {3, 4}}. The elements of B are not 1, 2, 3, and 4. Rather, there are only three elements of B, namely the numbers 1 and 2, and the set {3, 4}.
Empty Set
In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
An
Event
is a one or more outcome of an experiment.
Examples of Event
. When a number cube is rolled, 1, 2, 3, 4, 5, or 6 is a possible event.
experimental probability
Experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials.
In mathematics, the
factorial
of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
FAIRNESS
the state, condition, or quality of being fair, or free from bias or injustice; evenhandedness: I have to admit, in all fairness, that she would only be paid for part of ...
In probability theory, to say that two events are independent means that the occurrence of one does not affect the probability of the other.
Independent Events
independent events
Definition: Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.
independent variable
a variable that is manipulated (controlled) by the researcher and evaluated by its measurable effect on the dependent variable
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently
INTERSECTING SETS
Definition:
Given two sets A and B, the intersection is the set that contains elements or objects that belong to A and to B at the same time
We write A Ç B
Basically, we find A Ç B by looking for all the elements A and B have in common. We next illustrate with examples

Example #1.
To make it easy, notice that what they have in common is in bold
Let A = {1 orange, 1 pinapple, 1 banana, 1 apple} and B = { 1 spoon, 1 orange, 1 knife, 1 fork, 1 apple}
A Ç B = {1 orange, 1 apple}
INTERSECTION OF SETS
joint probability
A statistical measure where the likelihood of two events occurring together and at the same point in time are calculated.
The edges that form the lateral faces of a solid are called the
Lateral Edges.
In probability theory and statistics, the
marginal distribution
of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.
Two events are
mutually exclusive
if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.
out·come
noun \ˈau̇t-ˌkəm\
: something that happens as a result of an activity or process
Example; there are two possible outcomes in the study.
In mathematics, the notion of
permutation
relates to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order.
Probability
is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition of whose truth we are not certain.
relating to, measuring, or measured by the quantity of something rather than its quality.
quantitative
is an algorithm for generating a sequence of numbers that approximates the properties of random numbers.
random number generator
random sample
Random sampling is a sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has a known, but possibly non-equal, chance of being included in the sample.
In mathematical analysis, the word
region
usually refers to a subset of or that is open (in the standard Euclidean topology), connected and non-empty. A closed region is sometimes defined to be the closure of a region. Regions and closed regions are often used as domains of functions or differential equations.
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis.
In probability theory, the
sample space
of an experiment or random trial is the set of all possible outcomes or results of that experiment.
In mathematics, a
set
is a collection of distinct objects, considered as an object in its own right.
For

example
,
the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. Sets are one of the most fundamental concepts in mathematics.
Slant height
The slant height of a right circular cone is the distance from any point on the circle to the apex of the cone.
slicing
a part, portion, or share
SUBSET
In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a super set of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
THREE-DIMENSIONAL
An object that has height, width and depth, like any object in the real world.

Example: your body is three-dimensional.

Also known as "3D".
TREE DIAGRAM
A tree diagram is a graphic organizer used to list all possibilities of a sequence of events in a systematic way. Tree diagrams are one method for calculating the total number of outcomes in a sample space.
TWO-WAY-TABLE
A two-way or contingency table is a statistical table that shows the observed number or frequency for two variables, the rows indicating one category and the columns indicating the other category.
two-dimensional
Having only two dimensions, especially length and width.
Lacking the requisite or expected range or depth:
two-way frequency table
A Frequency Table is a table that lists items and uses tally marks to record and show the number of times they occur.
union
A union of two sets is the set that contains all the elements that are in any of the original sets.
UNIVERSAL SET
In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a set of all sets leads to a paradox (Russell's paradox). However, some non-standard variants of set theory include a universal set.
Venn diagram
A Venn diagram or set diagram is a diagram that shows all possible logical relations between a finite collection of sets. Venn diagrams were conceived around 1880 by John Venn.
angle bisector
; A line which cuts an
angle into two equal halves

arc length
; The distance along the curved line making up the arc

arc
; a part of the circumference of a
circle or other curve.

area
; In mathematics the area of a plane figure refers to the number of square units the figure covers.

area formulas;
Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a".
Be careful!! Units count. Use the same units for all measurements.
Examples
square = a 2
rectangle = ab
parallelogram = bh
trapezoid = h/2 (b1 + b2)
circle = pi r 2
ellipse = pi r1 r2
area of a circle;
The area of a circle is the number
of square units inside that circle.

central angle;
A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B thereby subtending an arc between those two points whose angle is (by definition) equal to that of the central angle itself.


chord;
A line that links two points on a circle or curve. (pronounced "cord")

CIRCLE
A circle is a simple shape of Euclidean geometry that is the set of all points in a plane that are at a given distance from a given point, the center.

circumcenter;
Usually applies to a triangle, but also to regular polygons.
The point where the three perpendicular bisectors of the sides of a triangle meet. Also, the center of the circumcircle. One of a triangle's points of concurrency.


circumscribed angle;
a circumscribed literally means "to draw around". A circumscribed circle of a triangle
for example is the circle that passes through
all three vertices. Usually called the circumcircle.
circumscribe;
draw (a figure) around another, touching it at points but not cutting it.

concurrent;
meeting or intersecting in a point


coordinate plane;
The plane containing the "x" axis and "y" axis.


directed line segment;
A directed line segment is a portion of a line that has both a magnitude and direction.

incenter;
the center of the
incircle of a triangle or other figure.


inscribed angle;
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle.

inscribed arc;
An inscribed angle is said to intersect an arc on the circle. The arc is the portion of the circle that is in the interior of the angle. The measure of the intercepted arc (equal to its central angle) is exactly twice the measure of the inscribed angle.

inscribed quadrilateral;
An inscribed quadrilateral is any four sided figure whose vertices all lie on a circle. (The sides are therefore chords in the circle!)
INSCRIBE
to draw within a figure so
as to touch in as many places
as possible
<a regular polygon inscribed in a circle>
major arc;
A major arc (right figure) is an arc of a circle having measure greater than or equal to ( radians).
minor arc;
A minor arc (left figure) is an arc of a circle having measure less than or equal to ( radians).

partition;
the action or state of dividing or being divided into parts.

point of tangency
;
is the point where a tangent line touches a circle. It does not intersect, but rather touches at a single point

secant;
the ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine. A straight line that cuts a curve in two or more parts.


In mathematics (and more specifically geometry), a
semicircle
is a one-dimensional locus of points that forms half of a circle.
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