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Math 9 Glossary Abscissa - the first element in an ordered pair - it is the distance along the horizontal axis in the coordinate plane Acute Angle - an angle whose measure is between 0 and 90 Acute Triangle - a triangle with 3 acute angles Adjacent Angles - two angles that share a vertex and a common side but no common interior points Alternate Angles - two non-adjacent angles that lie on opposite sides of the transversal (when lines are cut by a transversal) - if the angles are between the lines they are called Alternate Interior Angles - if the angles are outside of the lines they are called Alternate Exterior Angles - Property: If parallel lines are cut by a transversal, then alternate interior angles are equal Altitude of a Triangle - the line segment drawn from any vertex of the triangle perpendicular to the line containing the opposite side - also called the Height of the triangle Axis (plural: Axes) - the horizontal and vertical number lines that form a coordinate plane - the horizontal number line is called the x-axis - the vertical number line is called the y-axis Base of a Triangle - any side of a triangle Binomial - an expression consisting of 2 terms Bisector of an Angle - a segment that divides an angle into 2 equal, adjacent angles Bisector of a Segment - a line, segment, ray, or plane that divides a segment into 2 equal segments Capacity - the amount of liquid that a container holds (usually measured in litres) Central Angle of a Circle - an angle whose vertex is the center of a circle and whose sides are radii of the circle Central Angle of a Regular Polygon - an angle formed at the center of a regular polygon by segments drawn from consecutive vertices Chord - a segment joining 2 points on a circle Circumference - the distance around a circle Coefficient - the numerical factor of a term Commission - earnings based on the amount of total sales Compatible Numbers - numbers that are easy to manipulate mentally Complementary Angles - two angles whose measures have the sum of 90 Composite Number - a whole number that has more than 2 different factors - the smallest composite number is 4 Concave Polygon - a polygon with at least one interior angle having a measure greater than 180 Congruent Figures - figures that have the same size and shape - triangles that have all corresponding sides/angles equal are called Congruent Triangles Convex Polygon - a polygon with no line containing a side of the polygon also containing a point in the interior of the polygon - a polygon with each interior angle measuring less than 180 Coordinate Plane - two number lines drawn perpendicular to one another and intersecting at their zero points - also called the Cartesian Coordinate System (after its inventor Rene Descarte) Coordinates - the ordered pair that names the location of a point in the coordinate plane - the first coordinate of an ordered pair is called the Abscissa - the second coordinate of an ordered pair is called the Ordinate Corresponding Angles - angles that have the same relative positions in relation to 2 given lines, segments, or rays - Property: if 2 parallel lines are cut by a transversal, then corresponding angles are equal - Property: if 2 triangles are congruent or similar, then corresponding angles are equal Cube - a product in which a number is multiplied by itself 3 times Cube Root - a number that when multiplied by itself 3 times gives the required number Data - the numerical information collected - data presented in the order it is collected is called Raw Data - data that has been rearranged and presented according to class/kind is called Sorted Data Degree Of A Variable - the number of times the variable occurs as a factor (equal to the exponent of the variable) Degree Of A Monomial - the sum of the number of times each variable occurs as a factor - the sum of the degrees of all variables in the monomial (sum of the exponents of all variables) Degree Of A Polynomial - the greatest of the degrees of the monomials in the simplest form of the polynomial Diagonal - a segment joining 2 non-consecutive vertices of a convex polygon Diameter - a chord that passes through the center of a circle (also: the length of this chord) - a segment that joins 2 points on a circle and passes through the center of the circle (also: the length of this segment) Divisibility Rules - patterns that allow you to determine whether a number divides evenly into another number (leaving no remainder) without actually doing the division Equation - a mathematical sentence containing an equal (=) sign Equiangular Triangle - a triangle with all angles equal (to 60) Equilateral Triangle - a triangle with all sides equal Estimation - determining an approximate amount, value, or size of some quantity Exponent - a number that indicates the number of times a base is used as a factor in a power Expression - a symbol or group of symbols that represent a mathematical quantity Exterior Angle Of A Convex Polygon - the angle outside a polygon formed by extending one of the sides of the polygon Face - any of the flat surfaces of a solid - any 2 faces that are parallel, congruent polygons are called Bases - the faces that are not bases are called Lateral Faces Factor Tree - a systematic way of determining the prime factors of a number Fraction - any number that can be written in the form a b where “a” and “b” are integers and “b” 0 - the number “a” is called the Numerator - the number “b” is called the Denominator Height Of A Triangle - the line segment drawn from any vertex of the triangle perpendicular to the line containing the opposite side - also called the Altitude of the triangle Height Of A Prism - the distance between the bases of a prism Height Of A Cone/Pyramid - the perpendicular distance between the Base and the vertex of the cone/pyramid Hypotenuse - the side opposite the right angle in a right triangle - the longest side in a right triangle Improper Fraction - a fraction whose numerator is equal to or greater than its denominator Inequality - a mathematical sentence that contains one of the inequality signs (, , . , ) Integer - any number in the following set {..., -3, -2, -1, 0, 1, 2, 3, ... } Interior Angles Of A Polygon - angles inside a polygon formed by the intersection of 2 sides of the polygon Interest - money paid for the use of someone else’s money - Simple Interest is calculated using the formula I = Prt - Compound Interest is calculated by adding the interest to the principal each time interest is calculated Isosceles Triangle - a triangle with (at least) 2 sides equal - the equal sides are called the Legs - the other side is called the Base Isosceles Trapezoid - a trapezoid with equal legs Like Terms (Similar Terms) - terms with exactly the same variable part or no variable part at all Mean - in statistics, the measure of central tendency calculated by adding all of the values and dividing (the sum) by the number of values - also called an Average Median - in statistics, the measure of central tendency that is the middle number when the values are arranged in increasing order - if there is an even number of pieces of data, the median is the average of the middle 2 pieces of data Median Of A Triangle - the line segment form any vertex of a triangle to the midpoint of the opposite side Median Of A Trapezoid - the segment that joins the midpoints of the legs of a trapezoid - Property: its length is half the sum of the Bases of the trapezoid Mixed Number (Mixed Fraction) - a number consisting of a whole number and a fraction Mode - in statistics, the value that appears most frequently in a set of data - if all values in the data set appear only once, that data set has no mode - it is possible for a data set to have more than one mode (if 2 or more pieces of data all occur the most number of times) Monomial - an expression that contains only one term - a number, variable, or the product of numbers and variables Obtuse Angle - an angle whose measure is between 90 and 180 Obtuse Triangle - a triangle that contains exactly one obtuse angle Opposites (Additive Inverses) - two numbers whose sum is zero Ordered Pair - a pair of numbers that gives the location of a point in a plane - always written in the form: (x,y) - the x-value (first coordinate) is called the Abscissa - the y-value (second coordinate) is called the Ordinate Ordinate - the y-value (second coordinate) of an ordered pair Parallelogram - a quadrilateral with both pairs of opposite sides parallel Percent - out of 100 Perpendicular - two lines, segments, rays, or planes that meet to form equal, adjacent, right (90) angles Pi () - the ratio of the circumference to the diameter in any circle 22 - its approximate value is 3.14 or 7 Polygon - a closed figure made up of line segments - a figure formed by coplanar segments such that: (1) each segment intersects exactly 2 other segments at their endpoints (2) no 2 segments with a common endpoint are in the same line Polynomial - an expression that contains one or more terms Population - in statistics, the entire group about which data is being collected - a (large) group of people or things used as a base in statistical measurement Power - a product in which all factors are the same Prime Number - a number (greater than one) whose only factors are itself and one - the smallest prime number is 2 Prism - a geometric solid with 2 bases that are congruent, parallel polygons and all other (lateral) faces that are parallelograms - if the lateral faces are rectangles the prism is called a Right Prism (otherwise the prism is called an Oblique Prism) - the Height of a prism is the perpendicular distance between the bases - a prism is named according to the shape of its bases Proper Fraction - a fraction whose numerator is less than its denominator Proportion - an equation that states 2 fractions/ratios are equal a c - example: or a:b = c:d b d - in the above proportion, “a” and “d” are called the Extremes of the proportion and “b” and “c” are called the Means of the proportion - the Law Of Proportions states: the product of the extremes is equal to the product of the means Protractor - a device used to measure angles (from 0 to 180) Pythagorean Theorem - in any right triangle, the square of (the length) the hypotenuse is equal to the sum of the squares of (the lengths) of the legs Pyramid - a geometric solid with one base that is a polygon and all other (lateral) faces are triangles with a common vertex - the Height of a pyramid is the perpendicular distance between the base and the vertex - a pyramid is named according to the shape of its base Quadrant - one of the 4 regions that a Coordinate Plane is divided into (by the x and y axes) - the quadrants are labelled as follows: Quadrant 1 (I): top right Quadrant 2 (II): top left Quadrant 3 (III): bottom left Quadrant 4 (IV): bottom right Radius (plural: Radii) - the distance from the center of a circle to any point on the circle - the segment from the center of a circle to any point on the circle Range - is statistics, the difference between the greatest and the least values in a set of data Rate - a comparison of 2 quantities with different units of measure - a rate in which the second unit is one is called a Unit Rate Ratio - a comparison of 2 or more quantities with the same units of measure Rational Number - any number that can be written in the form a b where “a” and “b” are integers and “b 0” Reciprocals (Multiplicative Inverses) - two numbers whose product is one Reflex Angle - an angle whose measure is between 180 and 360 Regular Polygon - a polygon with all sides equal and all angles equal - a polygon that is both equilateral and equiangular Repeating Decimal - a decimal that contains a digit or block of digits that repeat unendingly - example: 0.3 = 0.333 ... 0.285 = 0.285 285 285 ... 6.497 = 6.497 979 797 ... Rhombus - a quadrilateral with all sides equal Right Triangle - a triangle that contains at most one right (90) angle - the side opposite the right angle is called the Hypotenuse (the longest side in a right triangle) - the other sides are called Legs Sample - in statistics, a representative portion of the population about which data is being collected - a (small) group of people or things used to represent a population - an important requirement of a sample is that it is a Random Sample (each member of the population has an equally likely chance of being selected for the sample) Scale Factor - the ratio of the distance measured on a scale drawing to the corresponding distance measured on the actual object Scalene Triangle - a triangle with no equal sides (all sides having different lengths) Scientific Notation - writing a number as the product of a number greater than or equal to 1 and less than 10 and the appropriate power of ten - example: 118 000 = 1.18 x 105 0.000 45 = 4.5 x 10-4 Secant (of a circle) - a line that intersects a circle in 2 points Similar Polygons - polygons that have the same shape but not necessarily the same size - polygons whose vertices can be paired so that: (1) corresponding angles are equal (2) corresponding sides are in proportion Simplify - to replace an expression with the simplest or most common form of its value - involves following properties of algebra like removing brackets, order of operations, etc. Simplified Fraction - a fraction whose numerator and denominator only have a common factor of one Solve - to find the solution set of an equation over a given set of replacement values (domain) - to find the value(s) that satisfy a given equation Square - a product in which a number is multiplied by itself Square Root - a number that when multiplied by itself gives the required number Straight Angle - an angle whose measure is 180 Supplementary Angles - two angles whose measures have the sum of 180 Surface Area - the sum of the areas of all the faces, including the bases, of a three dimensional object - the amount of material needed to build a solid Term - a number, variable, or the product or quotient of numbers and variables Transformations - used to solve equations - the procedure of moving terms from one side of the equation to the other side of the equation (by doing the same thing to both sides of the equation) until eventually the variable is isolated on one side of the equation Transversal - a line that intersects 2 or more other coplanar lines in different points Trapezoid - a quadrilateral with exactly one pair of parallel sides Trinomial - an expression consisting of 3 terms Unit Rate - a rate in which the second term is “1” Variable - a symbol, usually a lowercase letter, that is used to represent a number Vertex (plural: Vertices) - the point of intersection of 2 rays that form an angle, 2 sides of a polygon, or 2 edges of a solid Vertical Angles (Vertically Opposite Angles) - two angles with a common vertex and if placed together form 2 pairs of opposite rays - two angles formed by the intersection of 2 lines that share a common vertex but no common sides or interior points - Property: Vertical angles are equal