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# IMC4 WGU

### Math

Question | Answer |
---|---|

Acute Angle | An angle that has measure less than 90°. |

Angle Bisector | A line or ray that divides an angle in half. For polygons, an angle bisector is a line that bisects an interior angle. |

Algebraic Expression | Real numbers that can occur as roots of polynomial equations that have integer coefficients. For example, all rational numbers are algebraic. |

Algorithm | way of setting out a step by step mathematical procedure |

Alternate Interior Angles | Alternate interior angles are congruent. Formally, alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. |

Angle | Two rays sharing a common endpoint. Angles are typically measured in degrees or radians. |

Area | The size a surface takes up. Measured in square units. |

Associative property | Any operation for which (ab)c = a(bc) for all values of a, b, and c. Addition and multiplication are both associative. Subtraction and division are not. |

Commutative property | Any operation for which ab = ba for all values of a and b. Addition and multiplication are both commutative. Subtraction, division, and composition of functions are not. For example, 5 + 6 = 6 + 5 but 5 – 6 ≠ 6 – 5. |

Complementary Angles | Two acute angles that add up to 90°. For example, 40° and 50° are complementary. In the diagram below, angles 1 and 2 are complementary. |

Constant | Term or expression with no variables. Also, a term or expression for which any variables cancel out. For example, –42 is a constant. So is 3x + 5 – 3x, which simplifies to just 5. That is, not changing or moving. |

Consecutive Interior Angles | Consecutive interior angles are supplementary. Formally, consecutive interior angles may be defined as two interior angles lying on the same side of the transversal cutting across two parallel lines. |

Cube | A regular polyhedron for which all faces are squares. Note: It is one of the five platonic solids. |

Congruent | Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. they are the same. |

Corresponding Parts of Congruent Triangles are Congruent (CPCTC) | A theorem stating that if two triangles are congruent, then so are all corresponding parts. |

Repeating Decimal | A decimal that has repeating digits. |

Terminating Decimal | A decimal that has a finite (limited) number of digits. |

Distribute property | To multiply out the parts of an expression. Distributing is the opposite of factoring. |

Equilateral Triangle | A triangle with three congruent sides. Note: The angles of an equilateral triangle are each 60°. |

Equation | A mathematical sentence built from expressions using one or more equal signs. |

Evaluate | To figure out or compute. For example, "evaluate" means to figure out that the expression simplifies to 17. |

Expanded Notation | A way of writing number to show place value. |

Exponential Form | A function of the form y equals a•bx where a > 0 and either 0 < b < 1 or b > 1. The variables do not have to be x and y. For example, A equals 3.2•(1.02)t is an exponential function. |

Exterior Angle of a Polygon | An angle between one side of a polygon and the extension of an adjacent side. Note: The sum of the exterior angles of any convex polygon is 360°. This assumes that only one exterior angle is taken at each vertex. |

Fraction | A ratio of numbers or variables. Fractions may not have denominator 0. |

Greatest Common Factor (GCF)/ Greatest Common Divisor (GCD) | The largest integer that divides evenly into each of a given set of numbers. Often abbreviated GCF or gcf. For example, 6 is the gcf of 30 and 18. Sometimes GCF is written using parentheses: (30, 18) = 6. |

Hypotenuse | The side of a right triangle opposite the right angle. Note: The hypotenuse is the longest side of a right triangle. |

Hypotenuse leg | Either of the sides in a right triangle opposite an acute angle. The legs are the two shorter sides of the triangle. |

Inequality | Definition 1: Any of the symbols <, >, ≤, or ≥. Definition 2: A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥. |

Interior Angle | An angle on the interior of a plane figure. parallel lines cut by a transversal. Note: The sum of the interior angles of an n-gon is given by the formula (n – 2)•180°. For a triangle this sum is 180°, a quadrilateral 360°, a pentagon 540°, etc. |

Isosceles Triangle | A triangle with two sides that are the same length. Formally, an isosceles triangle is a triangle with at least two congruent sides. If two sides of a triangle are congruent, then the angles opposite those sides are congruent. |

Integers | All positive and negative whole numbers (including zero). That is, the set {... , –3, –2, –1, 0, 1, 2, 3, ...}. |

Intersecting lines | Share one point and determine a plane. |

Irrational Number | A set of #'s on a # line that are not rational. A square root of a number that is not a perfect square or a decimal that neither terminates nor repeats. |

Least Common Multiple (LCM) | The smallest positive integer into which two or more integers divide evenly. For example, 24 is the LCM of 8 and 12. Sometimes the LCM is written using brackets: [8, 12]= 24. |

Line Segment | All points between two given points Including the given points themselves. |

Mass | The quantity of matter in an object. Often called weight but NOT the same. |

Mean | Add all the numbers together and then divide by the total of numbers added. 5+8+16+3 Equals 32 32/4 =8 The mean is 8. |

Median | Put numbers in order from smallest to greatest. The number in the middle of an odd amount of numbers is the median. 5, 10, 43, 55, 82 median is 43 |

Modes | The number in a set that repeats. If no number repeats then there is no mode. 275, 56, 37, 102,102 mode is 102 |

Obtuse Angle | An angle that has measure more than 90° and less than 180°. |

Parallel Lines | Two distinct coplanar lines that do not intersect and determine a plane. Note: Parallel lines have the same slope. |

Percent | Number out of 100 |

Perimeter | The distance around the outside of a plane figure. For a polygon, the perimeter is the sum of the lengths of the sides. |

Perpendicular | At a 90° angle. Note: Perpendicular lines have slopes that are negative reciprocals. Example: Perpendicular Lines |

Perpendicular Bisector | The line perpendicularAt (a 90° angle) to a segment passing through the segment's midpoint. Note: The perpendicular bisectors of the sides of a triangle are concurrent, intersecting at the circumcenter. |

Plane | A flat surface extending in all directions. Any three noncollinear points lie on one and only one plane. So do any two distinct intersecting lines. A plane is a two-dimensional figure. |

Point | The geometric figure formed at the intersection of two distinct lines. |

Probability | The likelihood of the occurrence of an event. The probability of event A is written P(A). Probabilities are always numbers between 0 and 1, inclusive. |

Properties of Equality Equation Rules definitions | 1. a = b means a is equal to b.2. a ≠ b means a does not equal b. |

Properties of Equality Equation Rules Operations | 1. Addition: If a = b then a + c = b + c.2. Subtraction: If a = b then a – c = b– c.3. Multiplication: If a = b then ac = bc. 4. Division: If a = b and c ≠ 0 then a/c = b/c. |

Reflexive Property | a = a |

Symmetric Property | If a = b then b = a. |

Transitive Property | If a = b and b = c then a = c. |

Pythagorean Theorem | An equation relating the lengths of the sides of a right triangle. The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. A^2 + B^2 = C^2 |

Random Sampling | A chance pick from a number of items, like drawing out of a hat. |

Rational Number | The set of all real numbers that can be written as a ratio of integers with nonzero denominator. |

Real Number | All numbers on the number line. This includes (but is not limited to) positives and negatives, integers and rational numbers, square roots, cube roots , π (pi), etc. |

Rectangle | A box shape on a plane. Formally, a rectangle is a quadrilateral with four congruent angles (all 90°). |

Reflection | A transformation in which a geometric figure is reflected across a line, creating a mirror image. That line is called the axis of reflection. |

Right Angle | A 90° angle. |

Rotation | A transformation in which a plane figure turns around a fixed center point. In other words, one point on the plane, the center of rotation, is fixed and everything else on the plane rotates about that point by a given angle. |

Rounding | A method of approximating a number using a nearby number at a given degree of accuracy. |

Rhombus | A parallelogram with four congruent sides. Note that the diagonals of a rhombus are perpendicular (as is the case with all kites). Note: A square is a special kind of rhombus. |

scalene Triangle | A triangle for which all three sides have different lengths. |

Scientific Notation | A standardized way of writing real numbers. In scientific notation, all real numbers are written in the form a•10b, where 1 ≤ a < 10 and b is an integer. For example, 351 is written 3.51•102 in scientific notation. |

Segment bisector | Cut into two congruent halves. A line, point or plane that divides something into two equal sections. |

Shift/Translation/Glide | A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or orientation. |

Similarity | Having the same shape but not necessarily the same size. |

Simple Closed Curve | A connected curve that does not cross itself and ends at the same point where it begins. Examples are circles, ellipses, and polygons. Note: Despite the name "curve", a simple closed curve does not actually have to curve. |

Skew lines | Have no intersecting point and do not determine a plane. |

Skip counting | Counting forwards or backwards in multiples or intervals of a given number. EX: counting by 2’s or 10’s |

Solution | Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities. |

Sphere | A three dimensional solid consisting of all points equidistant from a given point. This point is the center of the sphere. Note: All cross-sections of a sphere are circles. |

Square | A rectangle with all four sides of equal length. Formally, a square is a quadrilateral with four congruent sides and four congruent angles (all 90°). |

Statistics | The collection, organization, presentation, interpretation and analysis of data. Generic word of any kind of measurement or count. |

Surface Area | The total area of the exterior surface of a solid. Many formulas for the area of a surface are given below. |

Supplementary Angles | Two angles that add up to 180°. |

Symmetric | Describes a geometric figure or a graph consisting of two parts that are congruent to each other. |

Transversal | A line that cuts across a set of lines or the sides of a plane figure. Transversals often cut across parallel lines. Parallel lines cut by a transversal |

Trapezoid | A quadrilateral wit two parallel sides. The parallel sides are called the bases, and the other two sides are called the legs. |

Triangle | A polygon with three sides. The sum is 180 degrees. |

Triangle Sum Theorem | The sum of the interior angles of a triangle is 180 degrees. |

Third Angle Theorem | If two sets of corresponding angles in two triangles are congruent, the third angles are congruent. |

Right Triangle Corollary to the Triangle Sum Theorem | The acute angles of a right triangle are complementary. |

Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. |

SSS Triangle Congruence Postulate | If the corresponding sides of two triangles are congruent, the triangles are congruent. |

SAS Triangle Congruence Postulate | If two sets of corresponding sides and the included angles are congruent, the triangles are congruent. |

ASA Triangle Congruence Postulate | If two sets of corresponding angles and the included sides are congruent, the triangles are congruent. |

AAS Triangle Congruence Theorem | If two sets of corresponding angles and a set of corresponding non-included sides are congruent, the triangles are congruent. |

Truncate | A method of approximating a decimal number by dropping all decimal places past a certain point without rounding. For example, 3.14159265... can be truncated to 3.1415. |

Variable | A quantity that can change or that may take on different values. Variable also refers to a letter or symbol representing such a quantity. |

Vertical | Straight up and down. For example, a wall is vertical. |

Vertical Angles | Angles opposite one another at the intersection of two lines. Vertical angles are congruent. |

Volume | The total amount of space enclosed in a solid. |

Weight | Weight equals the mass of an object times the force of gravity. |

Whole Numbers | Nonnegative Integers 1, 2, 3, 4, |

Weight | Weight equals the mass of an object times the force of gravity. |

Whole Numbers | Nonnegative Integers 1, 2, 3, 4, |

Prime Number | A positive integer which has only 1 and the number itself as factors. For example, 2, 3, 5, 7, 11, 13, etc. are all primes. By convention, the number 1 is not prime. |

Composite Number | A positive integer that has factors other than just 1 and the number itself. For example, 4, 6, 8, 9, 10, 12, etc. are all composite numbers. The number 1 is not composite. |