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1 Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important concepts. Also available at BigIdeasMath.com: multi-language glossar vocabular flash cards Addition Propert of Equalit Adding the same number to each side of an equation produces an equivalent equation. adjacent angles Two angles that share a common side and have the same verte 7 = = and are adjacent. and are not adjacent. angle of rotation The number of degrees a figure rotates 80 R T T O S base (of a power) The base of a power is the common factor. See power. S R RST has been rotated 80 to R S T. center of dilation A point with respect to which a figure is dilated center of rotation A point about which a figure is rotated See dilation. See rotation. Copright Big Ideas Learning, LLC

2 center of a sphere The point inside a sphere that is the same distance from all points on the sphere See sphere. concave polgon A polgon in which at least one line segment connecting an two vertices lies outside the polgon congruent angles Angles that have the same measure congruent figures Figures that have the same size and the same shape congruent sides Sides that have the same length B G conve polgon A polgon in which ever line segment connecting an two vertices lies entirel inside the polgon A F Side AB and side FG are congruent sides. coordinate plane A coordinate plane is formed b the intersection of a horizontal number line and a vertical number line. Quadrant II -ais 5 Quadrant I -ais corresponding angles Matching angles of two congruent figures ABC DEF B E A C F D 5 O Quadrant III 5 5 Quadrant IV The origin is at (0, 0). Corresponding angles: A and D B and E C and F Copright Big Ideas Learning, LLC

3 corresponding sides Matching sides of two congruent figures ABC DEF B E A C F Corresponding sides: side AB and side DE side BC and side EF side AC and side DF D cube root A number that, when multiplied b itself, and then multiplied b itself again, equals a given number 8 = 7 = degree A unit used to measure angles 90, 5, dependent variable The variable whose value depends on the independent variable in an equation in two variables In the equation = 5 8, is the dependent variable. dilation A transformation in which a figure is made larger or smaller with respect to a fied point called the center of dilation A A C C O center of dilation B B A BC is a dilation of ABC with respect to the origin. The scale factor is. distance formula The distance d between an two, and points ( ) (, ) is given b the formula ( ) ( ). d = + (, ) d (, ) (, ) Division Propert of Equalit Dividing each side of an equation b the same number produces an equivalent equation. = 0 0 = = 0 enlargement A dilation with a scale factor greater than 9 A B A B C C O 5 6 ABC is an enlargement of ABC. Copright Big Ideas Learning, LLC

4 equation A mathematical sentence that uses an equal sign to show that two epressions are equal = 6, a + 7 = equivalent equations Equations that have the same solutions 8 = 0 and = 8 evaluate (an algebraic epression) Substitute a number for each variable in an algebraic epression. Then use the order of operations to find the value of the numerical epression. Evaluate + 5 when = 6. ( ) + 5 = = = eponent The eponent of a power indicates the number of times a base is used as a factor. See power. epression A mathematical phrase containing numbers, operations, and/or variables + 6, 8 +, 8 +, 6 a b eterior angles When two parallel lines are cut b a transversal, four eterior angles are formed t on the outside of the parallel lines. p q,, 5, and 6 are interior angles.,, 7, and 8 are eterior angles. eterior angles of a polgon The angles outside a polgon that are adjacent to the interior angles factor When whole numbers other than zero are multiplied together, each number is a factor of the product. =, so,, and are factors of. eterior angles Copright Big Ideas Learning, LLC

5 function A relation that pairs each input with eactl one output The ordered pairs ( 0, ), (, ), (, ), and (, 6 ) represent a function. Ordered Pairs ( 0, ) (, ) (, ), 6 ( ) hemisphere One-half of a sphere Input 0 Output 6 function rule An equation that describes the relationship between inputs (independent variable) and outputs (dependent variable) The function rule The output is three less than the input is represented b the equation =. hpotenuse The side of a right triangle that is opposite the right angle leg hpotenuse leg image The new figure formed b a transformation See translation, reflection, rotation, and dilation. independent variable The variable representing the quantit that can change freel in an equation in two variables In the equation = 5 8, is the independent variable. indirect measurement Indirect measurement uses similar figures to find a missing measure when it is difficult to find directl. B 60 ft 50 ft C D A 0 ft E 0 = = = 8 input In a relation, inputs are associated with outputs. inputs outputs ( 0, 0 ) (, ) (, ) Input 0 Output 0 The distance across the river is 8 feet. Copright Big Ideas Learning, LLC 5

6 integers The set of whole numbers and their opposites,,, 0,,,, interior angles When two parallel lines are cut b a transversal, four interior angles are formed on the inside of the parallel lines. See eterior angles. interior angles of a polgon The angles inside a polgon irrational number A number that cannot be written as the ratio of two integers π, interior angles joint frequenc Each entr in a two-wa table legs The two sides of a right triangle that form the right angle See hpotenuse. line of best fit A precise line of fit that best models a set of data Stud Time and Test Scores Test scores Stud time (minutes) line of fit A line drawn on a scatter plot close to most of the data points; It can be used to estimate data on a graph. Stud Time and Test Scores Test scores Stud time (minutes) 6 Copright Big Ideas Learning, LLC

7 line of reflection A line that a figure is reflected in to create a mirror image of the original figure See reflection. linear equation An equation whose graph is a line = O = linear function A function whose graph is a nonvertical line; a function that has a constant rate of change literal equation An equation that has two or more variables + 6 = mapping diagram A wa to represent a relation marginal frequencies The sums of the rows and columns in a two-wa table Input Output 5 6 Multiplication Propert of Equalit Multipling each side of an equation b the same number produces an equivalent equation. nonlinear function A function that does not have a constant rate of change; a function whose graph is not a line = 8 = 8 = = Copright Big Ideas Learning, LLC 7

8 ordered pair A pair of numbers (, ) used to locate a point in a coordinate plane; The first number is the -coordinate, and the second number is the -coordinate. (, ) origin The point, represented b the ordered pair (0, 0), where the horizontal the vertical number lines intersect in a coordinate plane See coordinate plane. O The -coordinate of the point (, ) is, and the -coordinate is. output In a relation, inputs are associated with outputs. See input. parallel lines Lines in the same plane that do not intersect; Nonvertical parallel lines have the same slope. All vertical lines are parallel. p q Indicates lines p and q are parallel. perfect cube A number that can be written as the cube of an integer 7, 8, 5 perfect square A number with integers as its square roots 6, 5, 8 perpendicular lines Lines in the same plane that intersect at right angles; Two nonvertical lines are perpendicular when the product of their slopes is. Vertical lines are perpendicular to horizontal lines. point-slope form A linear equation written in the form = m is in point-slope form. ( ) The line passes through the point ( ) the slope of the line is m.,, and = + 6 ( ) 8 Copright Big Ideas Learning, LLC

9 polgon A closed figure in a plane that is made up of three or more line segments that intersect onl at their endpoints power A product of repeated factors base eponent verte 5 = power is used as a factor 5 times. Power of a Power Propert To find a power of a power, multipl the eponents. Power of a Product Propert To find a power of a product, find the power of each factor and multipl. ( ) 8 = = m ( a ) n = a mn ( ) ( ab) 5 7 = 5 7 m m m = a b Product of Powers Propert To multipl powers with the same base, add their eponents. = = m n m+ n a a = a proportion An equation stating that two ratios are equivalent = 6 proportional Two quantities that form a proportion are proportional. Because and 6 and 6 are proportional. form a proportion, Pthagorean Theorem In an right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hpotenuse. a + b = c cm cm 5 cm 5 + = Copright Big Ideas Learning, LLC 9

10 Quotient of Powers Propert To divide powers with the same base, subtract their eponents. radical sign The smbol square root which is used to represent a a a m n = 9 = 9 7 m n = a, where a 0 5 = 5 9 = 7 ± 00 = ± 0 radicand The number under a radical sign The radicand of 5 is 5. radius of a sphere The distance from the center of a sphere to an point on the sphere See sphere. rate A ratio of two quantities with different units You read books ever weeks. ratio A comparison of two quantities using division; The ratio of a to b ( where b 0) can be written a as a to b, a : b, or. b to, :, or rational number A number that can be written as a b where a and b are integers and b 0 =, 0.5 =, = 5 5 = real numbers The set of all rational and irrational numbers, 6.5, π, 0 Copright Big Ideas Learning, LLC

11 reduction A dilation with a scale factor greater than 0 and less than 0 X 6 X Y Y reflection A transformation in which a figure is reflected in a line called the line of reflection; A reflection creates a mirror image of the original figure. K K line of reflection 6 O W W 8 6 Z Z L M N N O M L WXYZ is a reduction of WXYZ. regular polgon A polgon in which all the sides are congruent, and all the interior angles are congruent KLMN is a reflection of KLMN over the -ais. relation A relation pairs inputs with outputs and can be represented b ordering pairs on a mapping diagram. Ordered Pairs 0, ( ) (, ) (, ) Mapping Diagram Input Output 0 right angle An angle whose measure is 90 right triangle A triangle that has one right angle rise The change in between an two points on a line See slope. rotation A transformation in which a figure is rotated about a point called the center of rotation; The number of degrees a figure rotates is the angle of rotation. center of rotation R T T O S RST has been rotated about the origin O to R ST. S R Copright Big Ideas Learning, LLC

12 run The change in between an two points on a line See slope. scale factor (of a dilation) The ratio of the side lengths of the image of a dilation to the corresponding side lengths of the original figure See dilation. scatter plot A graph that shows the relationship between two data sets using ordered pairs in a coordinate plane Stud Time and Test Scores Test scores Stud time (minutes) scientific notation A number is written in scientific notation when it is represented as the product of a factor and a power of 0. The factor must be greater than or equal to and less than similar figures Figures that have the same shape but not necessaril the same size; Two figures are similar when corresponding side lengths are proportional and corresponding angles are congruent. similar solids Solids that have the same shape and proportional corresponding dimensions in. 9 in. in. in. 6 in. in. slope The slope m of a line is a ratio of the change in (the rise) to the change in (the run) between an, and, on a line. It is a two points ( ) ( ) measure of the steepness of a line. rise change in m = = run change in = slope = slope-intercept form A linear equation written in the form = m + b is in slope-intercept form. The slope of the line is m, and the -intercept of the line is b. The slope is and the -intercept is. (, 5) 5 (, ) = + (, ) (0, ) Copright Big Ideas Learning, LLC

13 solid A three-dimensional figure that encloses a space solution of an equation A value that makes an equation true 6 is the solution of the equation =. solution of a linear equation All of the points on a line solution of a sstem of linear equations An ordered pair that is a solution of each equation in a sstem (, ) is the solution of the following sstem of linear equations. = 7 + = 7 sphere The set of all points in space that are the same distance from a point called the center square root A number that, when multiplied b itself, equals a given number center radius, r The two square roots of 00 are 0 and 0. ± 00 = ± 0 standard form The standard form of a linear equation is a + b = c, where a and b are not both zero. Subtraction Propert of Equalit Subtracting the same number from each side of an equation produces an equivalent equation. + = = 0 0 = Copright Big Ideas Learning, LLC

14 sstem of linear equations A set of two or more linear equations in the same variables, also called a linear sstem. = + Equation = 7 Equation theorem A rule in mathematics The Pthagorean Theorem transformation A transformation changes a figure into another figure. See translation, reflection, rotation, and dilation. translation A transformation in which a figure slides but does not turn; Ever point of the figure moves the same distance and in the same direction. A C B O C A B ABC has been translated units left and units up to ABC. transversal A line that intersects two or more lines two-wa table Displas two categories of data collected from the same source transversal variable A smbol that represents one or more numbers verte (of an angle) The point at which the two sides of an angle meet is a variable in +. verte Copright Big Ideas Learning, LLC

15 verte (of a polgon) A point at which two sides of a polgon meet; The plural of verte is vertices. whole numbers The numbers 0,,,,, See polgon. -ais The horizontal number line in a coordinate plane See coordinate plane. -coordinate The first coordinate in an ordered pair, which indicates how man units to move to the left or right from the origin In the ordered pair (, 5 ), the -coordinate is. -intercept The -coordinate of the point where a line crosses the -ais -intercept = b -ais The vertical number line in a coordinate plane See coordinate plane. (0, b) -intercept = a O (a, 0) -coordinate The second coordinate in an ordered pair, which indicates how man units to move up or down from the origin In the ordered pair (, 5 ), the -coordinate is 5. -intercept The -coordinate of the point where a line crosses the -ais See -intercept. Copright Big Ideas Learning, LLC 5

Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression

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