K Geometry Definition – Glossary Of Mathematical Terms & Definition

The absolute value of a number is its distance from zero. For any x, |x| is defined as follows: | x |= x, if x > 0, and | x |= −x, if x

Acute Angle An angle whose measure is greater than 0 degrees and less than 90 degrees.

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Example of an acute angle

Acute Triangle A triangle in which all three angles are acute angles.

Addition Property of Equality If a= b, then a + c= b + c.

Additive Inverse For any number x, there exists a number −x, such that x + −x= 0.

Adjacent Angle Two angles that share a common vertex and a common side.

Altitude of a Triangle A segment drawn from a vertex of the triangle perpendicular to the opposite side of the triangle, called the base, (or perpendicular to an extension of the base).

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AD is an altitude of the triangle

Angle An angle is formed when two rays share a common vertex.

Area The surface area of a two-dimensional figure.

Area Model A mathematical model based on the area of a rectangle, used to represent multiplication or to represent fractional parts of a whole.

Arithmetic Sequence A sequence a1, a2, a3, a4,… is an arithmetic sequence if there is a number c such that for each n, an + 1= an + c, that is an + 1 – an = c.

Associative Property of Addition For any numbers x, y , and z: (x + y) + z= x + (y + z).

Attribute A distinguishing characteristic of an object such as angles or sides of a triangle.

Average See: Mean.

Axis A number line in a plane. Plural form is axes. Also see: Coordinate Plane.

Bar Graph A graph in which rectangular bars, either vertical or horizontal, are used to display data.

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Example of a bar graph

Base

If any number x is raised to the nth power, written as x^n, x is called the base of the expression; Any side of a triangle; Either of the parallel sides of a trapezoid; Either of the parallel sides of a parallelogram.

Box and Whisker Plot For data ordered smallest to largest the median, lower quartile and upper quartile are found and displayed in a box along a number line. Whiskers are added to the right and left and extended to the least and greatest values of the data.

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Example of a box and whisker plot

Cartesian Coordinate System See: Coordinate Plane.

Center of a Circle A point in the interior of the circle that is equidistant from all points of the circle.

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A circle and its center

Chord A segment whose endpoints are points on a circle.

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PQ is a chord of the circle

Circle The set of points in a plane equidistant from a point in the plane.

Circle Graph See: Pie graph.

Circumference The distance around a circle. Its length is the product of the diameter of the circle and pi.

Coefficient In the product of a constant and a variable the constant is the numerical coefficient of the variable and is frequently referred to simply as the coefficient.

Combining Like Terms nk + nm= n(k + m). Also commonly called factoring.

Common Denominator A common multiple of the denominators of two or more fractions. Also see: Least Common Denominator

Common Factor A factor that two or more integers have in common. Also see: Greatest Common Factor.

Common Multiple See: Least Common Multiple.

Commutative Property of Addition For any numbers x and y: x + y = y + x.

Commutative Property of Multiplication For any numbers a and b: ab= ba.

Complement The complement of a set is a set of all the elements of the universal set that are not in the given set.

Complementary Angles Two angles are complementary if the sum of their measures totals 90º.

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Complementary angles, a and b

Composite Number A prime number is an integer p greater than 1 with exactly two positive factors: 1 and p. A composite number is an integer greater than 1 that has more than two positive factors. The number 1 is neither a prime nor a composite number.

Compound Interest Interest added to the principal of an account, so that the added interest also earns interest going forward.

Compound Event See: Event.

Cone A three-dimensional figure with a circular base joined to a point called the apex.

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Example of a cone

Congruent Used to refer to angles or sides having the same measure and to polygons that have the same shape and size.

Conjecture An assumption that is thought to be true based on observations.

Constant A fixed value.

Constant of Proportionality If a function has a rule in the form y= Kx, then for any input x≠0, the quotient of y/x will always have the value K. The number K is called constant of proportionality.

Constant Rate Of Change y= mx + b, here m is the constant rate of change.

Constant Rate Of Proportionality Another term for scale factor.

Coordinate(s) A number assigned to each point on the number line which shows its position or location on the line. In a coordinate plane that ordered pair, (x,y), assigned to each point of the plane showing its position in relation to the x-axis and y-axis.

Coordinate Plane A plane that consists of a horizontal and vertical number line, intersecting at right angles at their origins. The number lines, called axes, divide the plane into four quadrants. The quadrants are numbered I, II, III, and IV beginning in the upper right quadrant and moving counterclockwise.

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Coordinate Plane

Corresponding Angles

If two lines are cut by a transversal the angles on the same side of the transversal and on the same side of the two lines are corresponding angles. If the lines are parallel the pairs of angles will have equal measure. If two polygons are similar the angles that are in the same relative position in the figures are corresponding angles and have equal measures.

Corresponding Sides If two polygons are similar the sides of the polygons in the same relative positions are corresponding sides and the ratio of the lengths of each pair is the same.

Counterclockwise A circular movement opposite to the direction of the movement of the hands of a clock.

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Counterclockwise direction

Counting Numbers The counting numbers are the numbers in the following never-ending sequence: 1, 2, 3, 4, 5, 6, 7… We can also write this as +1, +2, +3, +4, +5, +6, +7,… These numbers are also called the positive integers or natural numbers.

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Coupon A percentage discount or a fixed amount of money taken off the sale price of an item.

Cube

A three-dimensional shape having six congruent square faces. The third power of a number.

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Cube

Cylinder

A three-dimensional figure with parallel circular bases of equal size joined by a lateral surface whose net is a rectangle.

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Cylinder

Data A collection of information, frequently in the form of numbers. Each individual piece of information is called a data point.

Data Analysis The process of making sense of collected data.

Data Point See: Data.

Degree

The circumference of a circle is divided into 360 equal parts or arcs. Radii drawn to both ends of the arc form an angle of 1 degree. The degree of a term is the sum of the exponents of the variables. The degree of a polynomial is the highest degree of any of its terms.

Denominator The denominator of a fraction indicates into how many equal parts the whole is divided. The denominator appears beneath the fraction bar.

Dependent Variable The output values for a function.

Diameter A segment with endpoints on the circle that passes through its center.

Distributive Property n(k + m)= nk + nm.

Distance For any two numbers x and y, the distance between x and y is the absolute value of their difference; that is, Distance= |x – y|.

Dividend The quantity that is to be divided.

Divisibility Suppose that n and d are integers, and that d is not 0. The number n is divisible by d if there is an integer q such that n= dq. Equivalently, d is a factor of n or n is a multiple of d.

Division Algorithm Given two positive integers a and b, we can always find unique integers q and r such that a= bq + r and 0≤ r The quantity by which the dividend is divided.

Domain The set of input values in a function.

Edge A segment that joins consecutive vertices of a polygon or a polyhedron.

Elements Members of a set.

Empirical Probability Probability determined by real data collected from real experiments.

Empty set Also called a Null Set. A set that has no elements.

Equation A math sentence using the equal sign to state that two expressions represent the same number.

Equilateral Triangle An equilateral triangle is a triangle with three congruent sides. An equilateral triangle also has three congruent angles, which we can also call equiangular triangle.

Equivalent

A term used to describe equations or inequalities that have the same solution. A term used to describe fractions or ratios that are equal. A term used to describe fractions, decimals, and percents that are equal.

Event An event is any subset of the sample space. A simple event is a subset of the sample space containing only one possible outcome of an experiment. A compound event is a subset of the sample space containing two or more outcomes.

Experiment A repeatable action with a set of outcomes.

Experimental Probability See: Empirical Probability.

Expressions Mathematical phrases used to describe quantities.

Exponent Suppose that n is a whole number. Then, for any number x, the nth power of x, or x to the nth power, is the product of n factors of the number x. This number is usually written x^n. The number x is usually called the base of the expression x^n, and n is called the exponent.

Exponential Notation A notation that expresses a number in terms of a base and an exponent.

Face Each of the surface polygons that form a polyhedron.

Factor An integer that divides evenly into a dividend. Use interchangeably with divisor except in the Division Algorithm.

Factorial The factorial of a non-negative number n is written n! and is the product of all positive integers less than or equal to n. By definition 0!= 1!= 1.

Fraction Numbers of the form m/n, where n is not zero.

Frequency The number of times a data point appears in a data set.

Function A function is a rule which assigns to each member of a set of inputs, called the domain, a member of a set of outputs, called the range.

Graph of a Function The pictorial representation of a function.

Greater than, Less Than Suppose that x and y are integers. We say that x is less than y, x y, if x is to the right of y on the number line.

Greatest Common Factor, GCF Suppose m and n are positive integers. An integer d is a common factor of m and n if d is a factor of both m and n. The greatest common factor, or GCF, of m and n is the greatest positive integer that is a factor of both m and n. We write the GCF of m and n as GCF (m,n).

Height The length of the perpendicular between the bases of a parallelogram or trapezoid; also the altitude of a triangle.

Horizontal Axis See: Coordinate Plane.

Hypotenuse The side opposite the right angle in a right triangle.

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Hypotenuse of a right triangle

Improper Fraction A fraction in which the numerator is greater than or equal to the denominator.

Independent Events If the outcome of the first event does not affect the outcome of the second event.

Independent Variable The input values for a function.

Inequality A statement that one expression is less than or greater than another.

Input Values The values of the domain of a function.

Integers The collection of integers is composed of the counting numbers, their negatives, and zero; … −4, −3, −2, −1, 0, 1, 2, 3, 4…

Intersection of Sets A set whose elements are all the elements that the given sets have in common, written A ∩ B.

Irregular Polygon A polygon that is not a regular polygon.

Isosceles Triangle A triangle with at least two sides of equal length is called an isosceles triangle.

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Isosceles Triangle

Lateral Area The surface area of any three-dimensional figure excluding the area of any surface designated as a base of the figure.

Lattice Point A point of the coordinate plane, (x,y), in which both x and y are integers.

Law Of Large Numbers As the number of trials in an experiment are increased, the average of the experimental probability approaches the theoretical probability.

Least Common Denominator The least common denominator of the fractions p/n and k/m is LCM(n, m).

Least Common Multiple, LCM The integers a and b are positive. An integer m is a common multiple of a and b if m is a multiple of both a and b. The least common multiple, or LCM, of a and b is the smallest integer that is a common multiple of a and b. We write the LCM of a and b as LCM (a,b).

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Legs

The two sides of a right triangle that form the right angle. The equal sides of an isosceles triangle or the non-parallel sides of a trapezoid.

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Legs of a right triangle

Less Than See: Greater Than.

Line Graph A graph used to display data that occurs in a sequence. Consecutive points are connected by segments.

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Example of a line graph

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Example of a line plot

Linear Model for Multiplication Skip counting on a number line.

Magnitude The absolute value of a number; its distance from zero.

Mean The average of a set of data; sum of the data divided by the number of items. Also called the arithmetic mean or average.

Measures of Central Tendency Generally measured by the mean, median, or mode of the data set

Median The middle value of a set of data arranged in increasing or decreasing order. If the set has an even number of items the median is the average of the middle two items.

Missing Factor Model A model for division in which the quotient of an indicated division is viewed as a missing factor of a related multiplication.

Mixed Numbers The sum of an integer and a proper fraction.

Mode The value of the element that appears most frequently in a data set.

Multiplicative Inverse The number x is called the multiplicative inverse or reciprocal of the positive integer n if x · n= 1.

Multiplicity The number of times a factor appears in a factorization.

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Natural Numbers See: Counting Numbers.

Net Yardage Total number of yards gained or lost at the end of a series of plays in a sports game.

Negative Integers Integers less than zero.

Nets One way to see the surface area of a three dimensional figure by cutting along its edges to produce a two-dimensional figure.

Notation A technical system of symbols used to convey mathematical information.

Number Line Model A pictorial representation of numbers on a straight line.

Null Set See: Empty Set.

Numerator The expression written above the fraction bar in a common fraction to indicate the number of parts counted.

Obtuse Angle An angle whose measure is greater than 90 degrees and less than 180 degrees.

Obtuse Triangle A triangle that has one obtuse angle.

Opposite Angle The angle that is opposite to a given side of a plane figure.

Order Of Operations The order of mathematical operations, with computations inside parentheses to be done first, and addition and subtraction from left to right done last.

Ordered Pair A pair of numbers that represent the coordinates of a point in the coordinate plane with the first number measured along the horizontal scale and the second along the vertical scale.

Origin The point with coordinate 0 on a number line; the point with coordinates (0,0) in the coordinate plane.

Outcomes The set of possible results of an experiment.

Outlier A term referring to a value that is drastically different from most of the other data values.

Output Values The set of results obtained by applying a function rule to a set of input values.

Parallel Lines Two lines in a plane that never intersect.

Percent A way of expressing a number as parts out of 100; the numerator of a ratio with a denominator of 100.

Perfect Cube An integer n that can be written in the form n= k³, where k is an integer.

Perfect Square An integer n that can be written in the form n= k², where k is an integer.

Perimeter The perimeter of a polygon is the sum of the lengths of its sides.

Perpendicular Two lines or segments are perpendicular if they intersect to form a right angle.

Pi The ratio of the circumference to the diameter of any circle, represented either by the symbol π, or the approximation 22/7 or 3.1415926…

Pie Graph A graph using sectors of a circle that are proportional to the percent of the data represented.

Positive Integers See: Counting Numbers.

Power See: Exponent.

Prime Number See: Composite Number.

Prime Factorization The process of finding the prime factors of an integer. The term is also used to refer to the result of the process.

Prism A type of polyhedron that has two bases that are both congruent and parallel, and lateral faces which are parallelograms.

Probability In an experiment in which each outcome is equally likely, the probability P(A) of an event A is m/n where m is the number of outcomes in the subset A and n is the total number of outcomes in the sample space S.

Proof A reasoning to help establish a fact.

Proper Fraction A fraction whose value is greater than 0 and less than 1.

Proportion An equation of ratios in the form a/b = c/d, where b and d are not equal to zero.

Protractor An instrument used to measure angles in degrees.

Pyramid A type of polyhedron that has one face, called a base, and triangular lateral faces that meet at a point called the apex.

Pythagorean Theorem The formula that states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a² + b² = c².

Quadrant See: Coordinate Plane.

Quadrilateral A plane figure with four straight edges and four angles.

Quotient The result obtained by doing division. See the Division Algorithm for a different use of quotient.

Radical Notation A math symbol to denote the root of an expression, such as square roots.

Radius The distance from the center of a circle a point of the circle. Plural form is radii.

Range The difference between the largest and smallest values of a data set. See Function for another meaning of range.

Rate A rate is a division comparison between two quantities with different units. Also see Unit Rate.

Ratio A division comparison of two quantities with or without the same units. If the units are different they must be expressed to make the ratio meaningful.

Rational Number A number that can be written as a/b where a is an integer and b is a natural number.

Ray Part of a line that has a starting point and continues forever in only one direction.

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Rebate Money that the customer receives, typically from the manufacturer, after making a purchase.

Reciprocal See: Multiplicative Inverse.

Rectangular Prism A solid 3D object that has six faces, each face being a rectangle.

Reflection The transformation that moves points or shapes by “flipping” them across a line or axis; a mirror image of the original set of points. If B is the reflection of A in line L, then L is the perpendicular bisector of segment AB.

Regular Polygon A polygon with equal length sides and equal angle measures.

Relatively Prime Two integers m and n are relatively prime if the GCF of m and n is 1.

Remainder See: Division Algorithm.

Repeating Decimal A decimal in which a cycle of one or more digits is repeated infinitely.

Right Angle An angle formed by the intersection of perpendicular lines; an angle with a measure of 90º.

Right Triangle A triangle that has a right angle.

Root The nodes in a tree diagram to represent events.

Sale A reduction in the sale price of an item.

Sample Space The set of all possible outcomes of an experiment.

Scaffolding A method of division in which partial quotients are computed, stacked, and then combined.

Scale Factor If polygons A and B are similar and s is a positive number so that for each side of A with length k there is a corresponding side of B with length sk, then s is the scale factor of A to B.

Scalene Triangle A triangle with all three sides of different lengths is called a scalene triangle.

Scaling

A process by which a shape is reduced or expanded proportionally. Choosing the unit of measure to be used on a number line.

Scientific Notation A mathematical shorthand to represent large numbers.

Sector A region of a circle bounded by two radii and an arc of the circle which joins their endpoints.

Sequence A list of terms ordered by the natural numbers. The outputs of a function whose domain is the natural numbers or whole numbers.

Set A collection of objects or elements.

Set Model A representation of groups of objects.

Similar Polygons Two polygons whose corresponding angles have equal measures and whose corresponding side lengths form equal ratios.

Simple Event See: Event.

Simple Interest Interest (money) that one earns by investing money in an account.

Simplest Form of a Fraction A form in which the greatest common factor of the numerator and denominator is 1.

Simplifying The process of finding equivalent fractions to obtain the simplest form.

Skewed An uneven representation of a set of data.

Slant Height An altitude of a face of a pyramid or a cone.

Solution The value of the variable that makes the equation true.

Square Root For non-negative numbers x and y, y= x , read “y is equal to the square root of x,” means y² = x.

Standard Notation Mathematical notation that is commonly used.

Stem and Leaf Plot A method of showing the frequency of a certain data by sorting and ordering the values.

Straight Angle An angle with a measure of 180 degrees formed by opposite rays.

Subset Set B is a subset of set A if every element of set B is also an element of set A.

Subtraction Property of Equality If a= b, then a – c= b – c.

Supplementary Angles Two angles are supplementary if the sum of their measures totals 180º.

Surface Area The total area of all the faces of a polyhedron. The total of the lateral area and base area of a cone. The total of the lateral area and the two bases of a cylinder.

Term

Each member of a sequence. Each expression in a polynomial separated by addition and subtraction signs.

Terminating Decimal If a and b are natural numbers with b ≠ 0 and a ÷ b yields a finite quotient, the decimal formed is a terminating decimal.

Tessellation Tiling of a plane with some shape.

Theoretical Probability Probability based on mathematical law rather than a collection of data.

Translation A transformation that moves a figure along a line in a plane but does not alter its size or shape.

Transversal Any line that intersects two or more lines at different points.

Trapezoid A four sided plane figure with exactly one set of parallel sides.

Tree Diagram

A process used to find the prime factors on an integer. A method to organize the sample space of compound events.

Triangle A plane figure with three straight edges and three angles.

Triangle Sum Theorem The sum of the measures of the interior angles of any triangle is 180 degrees.

Trichotomy A property stating that exactly one of these statements is true for each real number: it is positive, negative, or zero.

Unit Fractions Fractions of the form 1/n

Union of Two Sets A set that contains all of the elements that appear in either of the given sets, written A ∪ B.

Unit Rate A ratio of two unlike quantities that has a denominator of 1 unit.

Universal Set A set containing all of the elements under consideration.

Variable A letter or symbol that represents an unknown quantity.

Venn Diagram A diagram involving two or more overlapping circles that aids in organizing data.

Vertex

The common endpoint of two rays forming an angle. A point of a polygon or polyhedron where edges meet.

Vertical Angles If two straight lines intersect at a point, then each line is divided into two rays. The angles formed by using opposite rays from each line are called vertical angles.

Vertical Angle Theorem If two lines intersect at a point P, then the vertical angles formed will always have the same measure.

Vertical Axis See: Coordinate Plane.

Volume A measure of space; the number of unit cubes needed to fill a three-dimensional shape.

Whole Numbers The whole numbers are the numbers in the following never-ending sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ….

x-axis The horizontal axis of a coordinate plane.

x-coordinate The first number provided in an ordered pair (a, b).

y-coordinate The second number provided in an ordered pair (a, b).

y-axis The vertical axis of a coordinate plane.

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Zero Pair For any natural number n, n + (−n) is called a zero pair because their sum is zero.

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