Saxon Algebra 2 Terms and Definitions Lessons A-58

axis

an imaginary line about which a body rotates.

proportion

A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways: two equal fractions, or, using a colon, a:b = c:d.

rational expression

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials.

right prism

A right prism is a geometric solid that has a polygon as its base and vertical sides perpendicular to the base.

abstract equations

An abstract equation is an equation that uses two or more variables. Neither variable can be solved unless the other variable is given. A simple example is y=x.

acute angle

An acute angle ("acute" meaning "sharp") is an angle smaller than a right angle (it is less than 90 degrees).

acute triangle

An acute triangle is a triangle with all three angles acute.

algebraic expression

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide).

terminal position

An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

value

A number or formula result.

irrational number

A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (√2) are irrational numbers.

like terms

"Like terms" are terms whose variables (and their exponents such as the 2 in 2x) are the same. In other words, terms that are "like" each other.

transversal

(of a line) intersecting a system of lines.

diagonal

(of a straight line) joining two opposite corners of a square, rectangle, or other straight-sided shape.

congruent

(of figures) identical in form; coinciding exactly when superimposed.

irregular polygon

A polygon that does not have all sides equal and all angles equal. A polygon is "regular" only when all angles are equal and all sides are equal, otherwise it is irregular.

isolating the radical

A "radical" equation is an equation in which at least one variable expression is stuck inside a radical, usually a square root. For instance, this is a radical equation: ... In general, you "solve" equations by "isolating" the variable; you isolate the variable by "undoing" whatever had been done to it.

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.

chord

A chord of a circle is a straight line segment whose endpoints both lie on the circle.

if-then statement

A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion.

denominate numbers

A denominate number is a type of concrete number with a unit of measure attached with it. For example, 5 inches is a denominate number because it has the unit inches after it.

right solid

A geometric solid whose sides are perpendicular to its base.

tangent

A line in the plane of a circle that intersects the circle in exactly one point.

line

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

secant

A line that intersects a circle in two points

definition

A method of informing that explains something by identifying its meaning

coefficient

A number multiplied by a variable in an algebraic expression.

transposition

A transposition is therefore a permutation of two elements. For example, the swapping of 2 and 5 to take the list 123456 to 153426 is a transposition

equilateral triangle

A triangle with three congruent sides

pascal

A unit of pressure equal to one newton per square meter

major arc

An arc of a circle whose measure is greater than 180 degrees.

minor arc

An arc of a circle whose measure is less than 180 degrees.

inscribed angles

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.

obtuse angle

An obtuse angle is a form of angle that measures wider than 90° and less than 180°.

obtuse triangle

An obtuse triangle is a triangle in which one of the angles is an obtuse angle.

primitive terms

In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience.

geometric solid

In mathematics, solid geometry is the traditional name for the geometry of three-dimensional Euclidean space.

adjacent angles

Adjacent angles are two angles that have a common vertex and a common side.

difference of two squares theorem

In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity.

syllogism

an instance of a form of reasoning in which a conclusion is drawn (whether validly or not) from two given or assumed propositions (premises), each of which shares a term with the conclusion, and shares a common or middle term not present in the conclusion

commutative property

Commutative property is one of the basic properties of numbers. The word "commute" means "exchange" or "swap over" Commutative property states that numbers can be added or multiplied in any order. That is: Commutative Property of Addition states that changing the order of addends does not change the sum.

consecutive sides

Consecutive sides are any two sides that meet at an endpoint or an angle. Recognizing consecutive sides is important for many functions in geometry, as it helps identify segments and angles.

gram atomic weight

Gram atomic mass is the mass, in grams, of one mole of atoms in a monatomic chemical element.

deductive reasoning

Deductive reasoning is a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true.

isosceles triangle

a triangle with at least two congruent sides

scalene triangle

a triangle with no congruent sides

line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

undefined terms

In geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These four undefined terms are point, curve, line and plane.

parallel lines

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

monomials

an algebraic expression consisting of one term.

binomials

an algebraic expression of the sum or the difference of two terms.

equivalent equations

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

linear combination method

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

element

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

trinomials

an algebraic expression of three terms.

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). Regular polygons may be convex or star.

inverse operations

Inverse operations are opposite operations that undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.

imaginary numbers

Numbers that cannot exist in the real world

straight angle

an angle of 180°

right angle

an angle of 90°, as in a corner of a square or at the intersection of two perpendicular straight lines.

QED

Q.E.D. is an initialism of the Latin phrase "quod erat demonstrandum", meaning "which is what had to be shown".

scientific notation

Scientific notation is a method of writing or displaying numbers in terms of a decimal number between 1 and 10, multiplied by a power of 10.

axiom

Self-evident truth requiring no proof; universally or generally accepted principle

corresponding sides

Sides that have the same relative positions in geometric figures.

elimination method

The elimination method for solving linear systems. Another way of solving a linear system is to use the elimination method. In the elimination method you either add or subtract the equations to get an equation in one variable.

zero factor theorem

The factor theorem is a theorem linking factors and zeros of a polynomial.

addition method

The first method of solving systems of linear equations is the addition method, in which the two equations are added together to eliminate one of the variables. Adding the equations means that we add the left sides of the two equations together, and we add the right sides together.

point of tangency

The point of tangency is the point at which a line touches an ellipse or circle, assuming that the line only makes contact at one point.

ratio

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

scale factor

The ratio of any two corresponding lengths in two similar geometric figures. Note: The ratio of areas of two similar figures is the square of the scale factor. The ratio of volumes of two similar figures is the cube of the scale factor.

reflex angle

The reflex angle is the larger angle. It is more than 180° but less than 360° If you choose the smaller angle you might have an Acute Angle, or an Obtuse Angle instead: The larger angle is a Reflex Angle, but the smaller angle is an Acute Angle.

inscribed angle

an angle whose vertex is on a circle and whose sides contain chords of the circle

valid argument

an argument whose structure connects its reasons to its conclusions in a reliable manner

slant height

The slant height of an object (such as a frustum, or pyramid) is the distance measured along a lateral face from the base to the apex along the "center" of the face.

congruent triangles

Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in size.

similar triangles

Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent.

consecutive vertices

Vertices of a polygon that include the endpoints of the same side.

linear equation

an equation between two variables that gives a straight line when plotted on a graph.

polynomial equation

an equation that contains only polynomial terms

polynomial

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

right cylinder

a cylinder where the segment joining the centers of the bases is an altitude

graph

a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

origin

a fixed point from which coordinates are measured, as where axes intersect.

plane

a flat surface on which a straight line joining any two points on it would wholly lie.

decimal fraction

a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of a decimal point.

theorems

a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.

conclusion

a judgment or decision reached by reasoning.

curve

a line or outline that gradually deviates from being straight for some or all of its length.

point

a location

pyramid

a monumental structure with a square or triangular base and sloping sides that meet in a point at the top, especially one built of stone as a royal tomb in ancient Egypt.

factor

a number or algebraic expression by which another is exactly divisible.

rectangular coordinates

a pair of coordinates measured along axes at right angles to one another.

segment

a part of a figure cut off by a line or plane intersecting it, in particular.

arc

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

polygon

a plane figure with at least three straight sides and angles, and typically five or more.

convex polygon

a polygon with all its interior angles less than 180°.

concave polygon

a polygon with one or more interior angles greater than 180°.

variables

a quantity that during a calculation is assumed to vary or be capable of varying in value.

sphere

a round solid figure, or its surface, with every point on its surface equidistant from its center.

theorem

a rule in algebra or other branches of mathematics expressed by symbols or formulae.

cone

a solid or hollow object that tapers from a circular or roughly circular base to a point.

median

a straight line drawn from any vertex of a triangle to the middle of the opposite side.

half line

a straight line extending from a point indefinitely in one direction only.

radius

a straight line from the center to the circumference of a circle or sphere.

diameter

a straight line passing from side to side through the center of a body or figure, especially a circle or sphere

cube

a symmetrical three-dimensional shape, either solid or hollow, contained by six equal squares.

right triangle

a triangle with a right angle.

ray

any of a set of straight lines passing through one point.

perpendicular

at an angle of 90° to a given line, plane, or surface.

oval

having a rounded and slightly elongated outline or shape, like that of an egg.

rectangular

denoting or shaped like a rectangle.

bisect

divide (a line, angle, shape, etc.) into two equal parts.

intersect

divide (something) by passing or lying across it.

vertical angles

each of the pairs of opposite angles made by two intersecting lines.

supplementary angles

either of two angles whose sum is 180°.

complementary angles

either of two angles whose sum is 90°.

evaluate

find a numerical expression or equivalent for (an equation, formula, or function).

right geometric solid

geometric solids whose sides are at right angles to the bases

circular

having the shape of a circle

mentally

in a manner relating to the mind.

-gon

in nouns denoting plane figures with a specified number of angles.

alternate angles

two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.

rules

one of a set of explicit or understood regulations or principles governing conduct within a particular activity or sphere.

percent

one part in every hundred.

triangular

shaped like a triangle; having three sides and three corners.

postulate

something accepted as true without proof; an axiom

property

something that describes the way something is.

units

standard quantities used to specify measurements

exterior angle

the angle between a side of a rectilinear figure and an adjacent side extended outward.

exterior angles

the angle between a side of a rectilinear figure and an adjacent side extended outward.

interior angle

the angle between adjacent sides of a rectilinear figure.

interior angles

the angle between adjacent sides of a rectilinear figure.

corresponding angles

the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

reflection

the conceptual operation of inverting a system or event with respect to a plane, each element being transferred perpendicularly through the plane to a point the same distance the other side of it.

rotation

the conceptual operation of turning a system around an axis.

perimeter

the continuous line forming the boundary of a closed geometric figure.

circumference

the enclosing boundary of a curved geometric figure, especially a circle

slope-intercept form

the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

vertex

the highest point; the top or apex

absolute value

the magnitude of a real number without regard to its sign.

sector

the plane figure enclosed by two radii of a circle or ellipse and the arc between them.

gram molecular weight

the quantity of a chemical compound equal to its molecular weight in grams; now usually replaced by the mole.

hypotenuse

the side of a right triangle opposite the right angle

angle

the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

rationalizing the denomonator

to eliminate radicals from a denominator or fractions from a radicand