## Basic Math and Pre-Algebra

**APPENDIX C. Glossary**

absolute value The distance of a number from zero, without regard to direction.

acute angle An angle that measures less than 90°.

acute triangle A triangle that has three acute angles.

addend The numbers that are added when addition is performed.

adjacent angles A pair of angles that have the same vertex and share a side, but do not overlap one another.

algorithm A list of steps necessary to perform a process.

alternate interior angles Two angles that are on opposite sides of a transversal and between the parallel lines.

altitude A line segment from a vertex of a triangle perpendicular to the opposite side.

angle Two rays with a common endpoint.

angle bisector A line, ray, or segment that passes through the vertex of an angle and cuts it into two angles of equal size.

angle bisector in a triangle A line segment from the vertex of an angle to the opposite side of the triangle that divides the angle into two congruent angles.

apothem A line segment from the center of a polygon perpendicular to a side.

arc A portion of a circle.

associative property A property of addition or multiplication that says that when adding or multiplying more than two numbers you may group them in different ways without changing the result.

base angles The angles at each end of the base, or noncongruent side, of an isosceles triangle.

binary operation A process that works on two numbers at a time.

binary system A place value system based on the number two.

canceling The process of simplifying a multiplication of fractions by dividing a numerator and a denominator by a common factor.

center A point associated with a circle, from which all points of the circle are equidistant.

central angle An angle with its vertex at the center of a circle and sides that are radii. chord A line segment that connects two points on a circle.

circle The collection of all points that sit at a certain distance, called the radius, from a set point, called the center, forms the shape called a circle.

circumference The distance around a circle.

circumscribed A polygon is circumscribed about a circle if the polygon surrounds the circle with each side tangent to the circle.

common denominator A multiple of the denominators of two or more fractions.

common fraction Fractions written as a quotient of two integers.

commutative property A property of addition or multiplication that says that reversing the order of the two numbers will not change the result.

compatible numbers Two numbers that add to ten.

complementary angles A pair of angles whose measurements total 90°.

composite number A whole number that is not prime because it has factors other than itself and 1.

concave polygon A polygon in which one or more diagonals falls outside the polygon.

concentric circles Circles with the same center.

cone A solid with a circular base and a lateral surface that slopes to a point.

congruent Two segments are congruent if they are the same length. Two angles are congruent if they have the same measure.

congruent triangles Two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent.

coordinate system A system that locates every point in the plane by an ordered pair of numbers, (x, y).

corresponding angles A pair of angles that are on the same side of a transversal and are both above or both below the parallel lines.

counting numbers The set of numbers {1, 2, 3, 4, ...} you use to count. The counting numbers are also called the natural numbers.

cross-multiplying Finding the product of the means and the product of the extremes of a proportion and saying that those products are equal.

cube A prism in which all the faces are squares.

cylinder A solid with two circles as parallel bases and a rectangle wrapped around to join them.

decimal fraction Fractions written in the base ten system with digits to the right of the decimal point.

decimal system A place value system in which each position in which a digit can be placed is worth ten times as much as the place to its right.

denominator The number below the division bar in a fraction that tells how many parts the whole was broken into, or what kind of fraction you have.

diameter The longest chord in a circle that passes through the center.

difference The result of a subtraction problem.

digit A single symbol that tells how many.

distributive property The distributive property says that for any three numbers a, b, and c, c(a + b) = ca + cb. The answer you get by first adding a and b and then multiplying the sum by c will be the same as the answer you get by multiplying a by c and b by c and then adding the results.

dividend In a division problem, the number that is divided by the divisor.

divisor In a division problem, the number you divide by.

equation A mathematical sentence, which often contains a variable.

equiangular triangle A triangle in which all three angles are 60°.

equilateral triangle A triangle in which all three sides are the same length.

exponent A small number written to the upper right of another number that tells how many of that number should be multiplied together.

extended ratio Several related ratios condensed into one statement. The ratios a:b, b:c, and a:c make the extended ratio a:b:c.

exterior angle The angle formed when one side of a triangle is extended.

extremes The first and last numbers of a proportion.

faces The polygons that connect to form a polyhedron. factor Each number in a multiplication.

factor tree A method of finding the prime factorization of a number by starting with one factor pair and then factoring each of those factors, continuing until no possible factoring remains.

fraction A symbol that represents part of a whole.

greatest common factor The greatest common factor of two numbers is the largest number that is a factor of both.

hypotenuse In a right triangle, the side opposite the right angle.

improper fraction A fraction whose value is more than one. The numerator is larger than the denominator.

inscribed A polygon is inscribed in a circle if each of its vertices lies on the circle.

inscribed angle An angle with its vertex on the circle and sides that are chords.

integers The set of numbers that includes all the positive whole numbers and their opposites, the negative whole numbers, and zero.

interest Money you pay for the use of money you borrow, or money you receive because you’ve put your money into a bank account or other investment.

interest rate The percent of the principal that will be paid in interest each year.

inverse operation An operation that reverses the work of another.

irrational numbers Numbers that cannot be written as the quotient of two integers.

isosceles trapezoid A trapezoid in which the nonparallel sides are the same length.

isosceles triangle A triangle with two sides that are the same length.

lateral area The total of the areas of the parallelograms surrounding the bases of a prism. The area of the rectangle that forms the curved surface of a cylinder. The area of the slanted surface of a pyramid or cone.

least common denominator The least common multiple of two or more denominators.

least common multiple The smallest number that has each of two or more numbers as a factor.

legs In a right triangle, the two sides that form the right angle.

like terms Terms that have the same variable, raised to the same power.

line A set of points that has length but no width or height.

line segment A part of a line, made up of two endpoints and all the points of the line between the endpoints.

linear pair Two adjacent angles whose unshared sides form a straight angle. major arc An arc larger than a semicircle.

mean The arithmetic average of a group of numbers, found by adding all the numbers and dividing by the number of numbers in the group.

mean of a proportion The two middle numbers in a proportion.

median of a triangle A line segment that connects a vertex to the midpoint of the opposite side.

median of a trapezoid The line segment that connects the midpoints of the two non-parallel sides of a trapezoid.

midpoint The point on the segment that divides it into two segments of equal length.

minor arc An arc smaller than a semicircle.

minuend In a subtraction problem, the number from which another number is subtracted.

mixed number A whole number and a fraction, written side by side, representing the whole number plus the fraction.

natural numbers The set of numbers {1, 2, 3, 4, ...} you use to count. The natural numbers are also called the counting numbers.

number line A line divided into segments of equal length, labeled with numbers, usually the integers. Positive numbers increase to the right of zero, and negative numbers go down to the left.

numerator The number above the bar in a fraction that tells you how many of that denomination are present.

obtuse angle An angle that measures more than 90° but less than 180°.

obtuse triangle A triangle that contains one obtuse angle.

ordered pair Two numbers, usually designated as x and y, that locate a point in a coordinate system.

order of operations An agreement among mathematicians that we perform operations enclosed in parentheses or other grouping symbols first and then evaluate exponents. After that, do multiplication and division as you meet them moving left to right, and finally do addition and subtraction as you meet them, moving left to right.

parallel lines Lines on the same plane that never intersect.

parallelogram A quadrilateral in which both pairs of opposite sides are parallel.

PEMDAS A mnemonic, or memory device, to help you remember that the order of operations is parentheses, exponents, multiplication and division, addition, and subtraction.

percent A ratio that compares numbers to 100. 42% means 42 out of 100, or 42:100.

perimeter The total of the lengths of all the sides of a polygon.

period A group of three digits in a large number. The ones, tens, and hundreds form the ones period. The next three digits are the thousands period, then the millions, the billions, trillions, and on and on.

permutation An arrangement or ordering of a group of objects.

perpendicular lines Lines that meet to form a right angle.

place value system A number system in which the value of a symbol depends on where it is placed in a string of symbols.

plane A flat surface that has length and width but no thickness.

point A position in space that has no length, width, or height.

polygon A closed figure made up of line segments that meet at their endpoints.

polyhedron A solid constructed from polygons that meet at their edges.

polynomial An expression formed by adding terms, each of which is a number times a power of a variable.

power of ten A number formed by multiplying several 10s. The first power of ten is 10. The second power of ten is 100, and the third power of 10 is 1,000.

prime factorization The prime factorization of a number is a multiplication that uses only prime numbers and produces the original number as its product.

prime number A prime number is a whole number whose only factors are itself and 1.

principal The principal is the amount of money borrowed or invested. The rate is the percent of the principal that will be paid in interest each year.

prism A prism is a polyhedron with two parallel faces connected by parallelograms.

product The result of the multiplication is the product.

proper fraction A proper fraction is one whose value is less than one, and an improper fraction is one whose value is more than one.

proportion A proportion is two equal ratios. The means of a proportion are the two middle numbers. The extremes are the first and last numbers.

protractor A protractor is a circle whose circumference is divided into 360 units, called degrees, which is used to measure angles.

pyramid A pyramid is a polyhedron composed of a polygon for a base surrounded by triangles that meet at a point.

Pythagorean theorem A mathematical relation that states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It is often expressed as a^{2} + b^{2} = c^{2}.

Pythagorean triple A Pythagorean triple is a set of three whole numbers a, b, and c that fit the rule a^{2} + b = c^{2}.

quadrilateral A quadrilateral is a polygon with four sides.

quotient The result of a division is called a quotient.

radius The collection of all points that sit at a certain distance, called the radius, from a set point, called the center, forms the shape called a circle.

rate A comparison of two quantities in different units, for example, miles per hour or dollars per day.

ratio A ratio is a comparison of two numbers by division.

rational numbers The set of all numbers that can be written as the quotient of two integers.

ray A ray is a portion of a line from one endpoint, going on forever through another point.

real numbers The name given to the set of all rational numbers and all irrational numbers.

reciprocal Two numbers are reciprocals if their product is 1. Each number is the reciprocal of the other.

rectangle A rectangle is a parallelogram with four right angles.

regular polygon A polygon is regular if all sides are the same length and all angles are congruent.

relatively prime Two numbers are relatively prime if the only factor they have in common is 1.

remainder The number left over at the end of a division problem. It’s the difference between the dividend and the product of the divisor and quotient.

rhombus A parallelogram in which all sides are congruent. A square is a parallelogram with four congruent sides and four right angles.

right angle An angle that measures 90°.

right prism A prism is a right prism if the parallelograms meet the bases at right angles. right triangle A triangle that contains one right angle.

ruler A line or segment divided into sections of equal size, labeled with numbers, called coordinates, used to measure the length of a line segment.

scale factor The scale factor of two similar triangles is the ratio of a pair of corresponding sides.

scalene triangle A triangle that has three sides of different lengths.

scientific notation A method for expressing very large or very small numbers as the product of a number between 1 and 10 and a power of 10.

secant A line that intersects the circle at two different points.

segment bisector A line or ray or segment that passes through the midpoint of a segment and divides a segment into two congruent segments.

semicircle An arc equal to half a circle.

sides of angle The rays with a common endpoint that form the angle.

similar triangles Two triangles are similar if each pair of corresponding angles is congruent and corresponding sides are in proportion.

slope The slope of a line is a number that compares the rise or fall of a line to its horizontal movement.

solving an equation An equation is a mathematical sentence that often contains a variable. Solving an equation is a process of isolating the variable to find the value that can replace the variable to make a true statement.

space The set of all points.

sphere The set of all points in space at a fixed distance from a center point.

square A parallelogram in which all sides are congruent. A square is a parallelogram with four congruent sides and four right angles.

square numbers Numbers created by raising a number to the second power.

standard form When a polynomial is written in standard form, the terms are ordered from highest to lowest degree.

straight angle A straight angle is an angle that measures 180°.

subtrahend In a subtraction problem, the number subtracted from the minuend.

sum The result of addition.

supplementary angles A pair of angles whose measurements total 180°.

surface area The total of the areas of all the faces of a solid.

tangent A line that touches a circle at only one point.

tangent circles Circles that touch at only one point.

term An algebraic expression made up of numbers, variables, or both that is connected only by multiplication.

transversal A line that intersects two or more other lines.

trapezoid A quadrilateral in which one pair of opposite sides is parallel.

unlike terms Terms with different variables, such as x and y.

variable A letter or symbol that takes the place of a number.

vertex of an angle The point at which the two rays that form the sides of an angle meet.

vertex of a polygon The point at which two sides of a polygon meet.

vertex angle The angle between the equal sides of an isosceles triangle.

vertical angles A pair of angles formed when two lines intersect, which have their vertices at the point where two lines intersect and do not share a side.

volume The volume of a solid is the measure of the space contained by the solid.

whole numbers The set of numbers {0, 1, 2, 3, 4, ...} formed by adding a zero to the counting numbers.

v-coordinate The first number in an ordered pair indicates horizontal movement.

y-coordinate The second number in an ordered pair indicates vertical movement.