QUARTERLY EXAM 2 Rules & Definitions Shormann Prealgebra

P5

(Parallel postulate) Given a line n and a point P not on that line, there exists in the plane of P and n and through P only one line m, which does not intersect line n.

Triangles

- In any triangle, the sum of the measures of the three interior angles equals 180°. - In any triangle, the angles opposite sides of equal lengths have equal measures, and vice-versa.

The sum of complementary angles

- The sum of complementary angles equals 90°. x + y = 90°

Angle relationships

- When two line segments intersect, the vertical (opposite) angles are equal.

The sum of supplementary angles

-The sum of supplementary angles equals 180°. x + y = 180°

Exchange rates (2020 rates) 1 United States Dollar (USD) =

0.92 Euros (European Union) 75.9 Rupees (India) 1.41 Dollars (Canada) 73.6 Rubles (Russia) 24.0 Pesos (Mexico) 0.83 Pounds (Great Britain) 1.56 Dollars (Australia) 107.1 Yen (Japan) 7.10 Yuan (China) 5.86 Reals (Brazil)

In algebra, you don't have to write the 1

1x = x, x/1 = x, and x¹=x.

1 mile

= 1.61 kilometers

probability (P) of a particular event occurring

= A fraction or decimal between 0 and 1 of the

P3

A circle may be drawn with any given center and any given radius.

set

A collection of things, usually numbers when used in a mathematical way.

postulate

A construction (drawing) of something, normally common to a particular science, that may not be obvious. Assumed to be true without proof.

algebra

A generalization of arithmetic, where letters representing numbers are combined according to the rules of arithmetic, often to solve for an unknown value.

rational number

A number that can be written as a ratio of integers. As decimal numbers, if the decimal places continue forever, they will have a recognizable repeating pattern.

irrational number

A number that cannot be written as a ratio of integers. They have no recognizable repeating pattern of decimals.

scale factor

A number that scales, or multiplies another number, usually in a proportional relationship.

triangle

A plane (2D) figure with three straight sides and three interior angles.

rate

A ratio of two measurements. Often, time is the second measurement. Speed, for example, is the ratio of distance traveled divided by amount of time traveled.

triangles by angles

A right triangle has one right angle, an obtuse triangle has one angle greater than a right angle, and an acute triangle has three acute angles.

axiom

A self-evident statement about something obvious, normally common to all sciences.

P2

A straight line extends an indefinite length in either direction.

congruent

A word used to describe two or more identical shapes. Two or more planar (2D) shapes are congruent if you can lay one on top of the other and they match up exactly.

P4

All right angles are equal to one another.

triangles by sides

An equilateral triangle has all sides congruent (and all angles equal 60°), an isosceles triangle has two sides congruent, and a scalene triangle has no sides congruent.

diameter

Any line segment drawn through the center of a circle and terminated in both directions by the circumference.

x⁰ = 1

Anything (except 0) raised to the power of 0 equals 1.

deductive reasoning

Applying rules. In mathematics, we apply rules in new situations to discover new rules and truths.

discover

Being the first to find or observe.

Temperature

F = 1.8C + 32 F = Fahrenheit, C = Celsius

In many story problems, "of " means "multiply," and "is" means "equal to." F • a = b is pronounced "F of a equals b."

F represents any fraction (or decimal). The equation is a memory aid that will help you solve fraction/decimal story problems.

x·x·x·x.........x = xⁿ

For example, x·x = x², x·x·x = x³, x·x·x·x = x⁴, etc.

Euclidean geometry

Geometry based on Euclid's axioms, postulates, and definitions. Most "math class geometry" is Euclidean geometry; we normally drop the prefix and simply call it "geometry."

semicircle

Half a circle.

radius

Half the diameter. Any line segment that begins at the center of a circle and terminates on the circumference.

proportional

Having a constant ratio

algebraic subtraction

If a and b are real numbers, then a-b = a + (-b), and -b is the opposite of b. Example: 5-3 = 5 + (-3)

Additive property of equality

If a, b, and c represent real numbers, and if a=b, then a + c = b + c. Also, c + a = c + b

A2

If equals be added to equals, the wholes are equal. If a = b and c = d, then a + c = b + d

A3

If equals be subtracted from equals, the remainders are equal. If a = b and c = d, then a - c = b - d

term

In algebra, a term represents one or more parts of an algebraic expression or equation. For example, see the following chart:

coefficient

In algebra, the number in front of a variable(s). For example, 3x² has a coefficient of 3.

closed circle(●)

In math, a closed circle on a graph or number line means "include this value."

open circle(○)

In math, an open circle on a graph or number line means "don't include this value."

formula

In mathematics, it usually refers to an equation that uses symbols. It is like an evaluate problem with an equals sign

Volume equivalent measures

Metric 1 cm³ = 1 mL 1000 mL = 1 L mL=milliliter L=liter English 8 oz = 1 C 4 C = 1 qt 4 qt = 1 gal oz=ounce, C=cup qt=quart gal=gallon English/metric volume conversion: 1 liter = 1.057 quarts

polynomial in one unknown

One term, or a sum of individual terms of the form axⁿ, where a is a real number, x is an unknown quantity, and n is a whole number. Examples include 3x² (monomial), 2a + 7 (binomial), and -1.223z⁵ + 3z² - z (trinomial).

Perimeter

Rectangle = 2 (l + w) Square = 4s Circle = 2πr = πD

analogy

Resemblance in some particulars between things otherwise unlike; similar.

Finding the absolute value of a number

The absolute value of a equals a, and the absolute value of -a also equals a. In other words, |a|=|-a|=a. When we "find the absolute value," we don't change the number, but if it is negative we remove the sign.

rhetoric

The art of speaking or writing effectively.

circumference

The distance around a circle. A circle's perimeter.

perimeter

The distance around any flat (two-dimensional) shape.π: Pronounced "pie," but spelled pi, π is simply the ratio of a circle's circumference to diameter.

inductive reasoning

The process of discovering rules. Scientific endeavors are inductive. Discovery of new mathematical relationships requires inductive reasoning.

creativity

The use of imagination or original ideas.

A5

The whole is greater than the part.

Euclid's 5 axioms, or common notions: A1

Things that are equal to the same thing are also equal to one another. If a = c and b = c, then a = b

A4

Things which coincide with one another are equal to one another. In other words, a = a (reflexive axiom)

bisect

To split something into two equal parts.

like terms

Two or more terms whose variables are exactly the same (same letters, same exponents for each letter). Like terms can have different coefficients.

Euclid's 5 postulates P1

Two, and only two points determine one unique straight line.

descriptive variable

Usually a letter, or letter and subscript that also means something. For example, if we were adding two parts, Part A and Part B, we might write this PA+PB. Or if we were adding cats and dogs, we might write C+D. In both cases, rather than just writing "x+y," the variables provide more description, and therefore help you directly relate to the problem. Descriptive variables are particularly helpful when creating equations from story problems.

Real number chart

We can divide real numbers into two main sets, rational and irrational.

absolute value

two vertical bars enclosing a number, like this: |a|.