MrPerezOnlineMathTutor.com

GLOSSARY OF MATH TERMS

ALGEBRA AND GEOMETRY

Word Definition Examples

A

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Absolute Value

Distance of a number from zero on a number line. The distance is taken as positive all the time.

For a variable:

If x < 0 then –a; if x>=0 then a.

Acute angle An angle that is between 0 and 90 degrees
Acute triangle A triangle with all acute angles.

If a number then its opposite

When you add both numbers they are equal to zero.

Adjacent angles If two angles have a common side, a common vertex and no common interior points then they are adjacent.
Adjacent arcs If two arcs are in the same circle or arc and they have exactly one point in common then they are adjacent.
Algebra Everything you learn in arithmetic but with variables besides the numbers.
Algebraic expression A given set of letters called variables, and real numbers called constants that are combined using addition, subtraction, multiplication, division and/or exponentiation.
Alternate exterior angles Alternate exterior angles in alternate sides of the transversal that cuts parallel lines.
Alternative interior angles Interior angles in alternate sides of the transversal that cuts parallel lines.
Altitude Height
Altitude of a triangle Perpendicular from the vertex to the line containing the opposite side of the triangle.
Angle Geometry shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.
Angle-angle similarity (triangles) AA when two triangles have two corresponding pairs of angles congruent.
Angle bisector If a ray divides an angle into two congruent angles, then the ray is an angle bisector.
Angle bisector and proportional segments In a triangle an angle bisector divides the side of a triangle in proportional segments to the two remaining sides.
Angle in standard position If an angle has its vertex at the origin and its initial side along the positive x-axis, then the angle is in standard position.
Angle of depression Angle of Elevation is the angle formed by the straight oblique line connecting a point in the horizontal and a point above the horizontal. As viewed by one observer for whose eye the horizontal is drawn.
Angles formed by secants and/or tangents intersecting at an exterior point of a circle. The angle formed by  secants and/or   tangents intersecting at an exterior point is given by half the positive difference of the two included intersected arcs in the circle.
Angle formed by a secant and a tangent intersecting at the point of tangency. The angle formed by a secant and a tangent intersecting at the point of tangency in the circle is given by half the measure of the included intersected arc.
Angle of Elevation Angle of depression is the angle formed by the straight oblique line connecting a point in the horizontal and a point below the horizontal. As viewed by one observer for whose eye the horizontal is drawn.
Angle Sum Theorem The sum of the interior angles in a triangle is 180°.
Apothem of a regular polygon Perpendicular distance from the center of the regular polygon to the midpoint at the side of the same.
Arc Curved segment in a circle.
Arc length Following the path of the circle the distance between the endpoints of the arc.
Area of a circle The area of a circle is equal to  pi times the square of the radius.
Area parallelogram Area of a parallelogram is the product of the base and the height.
Area of a rectangle Area of a rectangle is the product of the length and the width.
Area of a rhombus Area of a rhombus is half the product of the diagonals.
Area of a trapezoid Area of a trapezoid is the half the product of the height and the sum of the bases.
Area of a triangle Area of the triangle is half the product of the base and the height.
Arithmetic Mean Add two numbers and divide by 2 to obtain the arithmetic mean. If we have 6 and 10, then the arithmetic mean is 8.
Arithmetic Sequence A sequence in which the difference between any two consecutive terms is a constant.
Arithmetic series For an arithmetic sequence, the indicated sum of the terms.
Associative Property Grouping addends in a sum or factors in a product in different order does not affect the answer.
Asymptote If the graph of a function gets close to a line but never intersects with this then the line is an asymptote.
Axis of Symmetry A line on which a graph is reflected onto itself.

B

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z TOP

Bar Graph A graph we use to compare amounts using bars to show the data. Graph where data is shown in bars
Base angle of an isosceles triangle The angles next to the base of the isosceles triangle.
Base angles of a trapezoid Each one of the parallel sides of the trapezoid.
Base of an isosceles triangle The side included between the base angles of an isosceles triangle and opposite to the vertex angle.
Biconditional A conditional and the converse of this need to be true, in which case "if only if " is used with the hypothesis and the conclusion of the conditional to make the biconditional.
Binomial Expression that has two (bi) terms
Binomial Experiment A experiment that has only two possible outcomes Tossing one coin is binomial because you only get heads or tails
Binomial probability Finds probabilities of binomial experiments and uses the binomial theorem to find the probabilities.
Binomial Theorem If we expand (x + y)n and n is a positive integer then
(x + y)n= C0xn + C1xn-1y1 + C2xn-2y2 + ... + Cn-1x1yn-1 + Cnyn
Branch A piece of a discontinuous graph is a branch.

y = (x + 8)/(4 + x) has two branches
has a discontinuity at

x = -4

C

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z  TOP

Center In a circle, it is the point from which all the points in the circle are equidistant.
Central angle If an angle has as vertex in the center of a circle then the angle is a central angle.
Centroid Given the medians in a triangle; the intersection point is the centroid.
Certain Event An event whose probability is one (1) or 100%
Chord A segment inside the circle whose endpoints lie in the circumference of the circle.
Chord perpendicular to diameter. A chord that is perpendicular to the diameter of the circle is bisected together with its arc.
Chords intersecting in the interior of a circle. Two chords intersecting in the interior of a circle produce segments for which the product in one chord is equal to the product in the other chord.
Circle

It is made of the set of all points in a plane laying at a constant distant r from a given point called center. If the radius is r and the center at (h,k) then the equation of the circle is given by

(x-h)2 + (y-k)2 = r2

Circumcenter of a triangle Given the perpendicular bisectors of a triangle, the circumcenter is their point of concurrency.
Circumference It is the perimeter of the circle.
Circumscribed about A polygon is circumscribed about a circle if all the sides are tangent to the circle, and a circle is circumscribed about a polygon if all the vertices of this are on the circumference of the circle.
Circumscribed rectangle A rectangle in the interior of a circle, and whose vertices are in the circle.
Coefficient Coefficient 7z
z is the variable and 7 the coefficient.
Collinear If a set of points lie in the same line then they are collinear.
Collinear points All points that lie on the same straight line.
Combination Any arrangement in which order is not important.
Combined variation An equation that simultaneously combines direct and inverse variation.
Common difference The different between two consecutive terms of an arithmetic sequence, represented by d.
Common Factors If numbers, variables and products formed from prime factors appear in all the terms of an expression, then these are common factors of that expression.

If 4x3 - 8x2
then 4 and x2

are factors.

Common logarithm It is the base 10 logarithm
Common ratio The ratio between two consecutive terms in a geometric sequence, called r.
Commutative Property

Modifying the order of addends or factors in a expression does not affect the sum or product.

Order is not important when adding or multiplying.

Compass A tool that is used to draw circles and arcs.
Complementary angles Two positive angles that when added give 90 degrees
Completing the Square Method that finds the constant term in an incomplete perfect square trinomial of a second degree equation to solve it.
Complex Conjugate Theorem It states that if we have an imaginary root in  one variable polynomial with real coefficients, then we have another root at the complex conjugate of this root. So if we have a + bi, the other root is at a - bi.
Complex fraction A fraction in which the numerator and or the denominator have a fraction.
Complex Number Number of the form a + bi, where the real part is a and the imaginary part is bi; both a and b are real numbers and i is the square root of -1.
Complex number plane A plane with perpendicular number lines, where the horizontal is the real part of a complex number and the vertical one is the imaginary part.
Composite function Combination of 2 functions where the input of the second is the output of the first.
Composite solid (surface area) A solid made of several other solids together for which the surface area is the touchable surface around the solid.
Composite solid (volume) A solid made of several other solids together for which the volume is the addition of all the volumes together of the solids that is made of.
Composition Suppose two functions f and g, where the range of g is a subset of the domain of f. Then the composition of f of g is f[g(x)].
Compound inequality If two inequalities are combined by words "and" or "or" then they are compound inequalities.
Concave polygon If a polygon has diagonals that lie outside the polygon then the polygon is concave.
Concentric circles Circles that share the same center.
Conclusion In a "if p then q" statement is the part that follows the then, that is q.
Concurrent Refers to lines that intersect and the intersection point is the point of concurrency.
Congruent chords In congruent circles or in the same circle are chords that intersect congruent arcs.
Congruent right triangles Right triangles with all corresponding angles and sides congruent.
Congruent triangles Triangles with all corresponding angles and sides congruent.
Conditional Refers to an "if p then q" statement.
Conditional probability Probability that contains a condition that may limit the sample space of a given event. The usual notation is

P(A|B) which reads: "The probability of event B, given event A."  For any two events A and B part of the sample space, P(A|B) = P(A and B)/P(A).

Cone It is a 3-D figure with circular base, a vertex not in the plane of the circle, and has a curved surface connecting the base with the vertex. The altitude of the cone is the perpendicular segment that goes from the vertex to the plane containing the circle at the base. The height is the length of the altitude. The slant height is the length of the distance from the vertex to the edge of the base. For a right cone it is necessary that the altitude contains the center of the circle at the base.
Congruent If two objects have the same size and same shape then they are congruent. Congruent symbol is an equal sign with a tilde over it.
Congruent angles Angles that have the same measure are congruent.
Congruent arcs Are arcs in the same circle or in congruent circles that have the same arc length.
Congruent polygons If two polygons have congruent corresponding sides and congruent corresponding angles then they are congruent.
Congruent segments Congruent segments are segments with the same shape and length.
Conic section A figure that is obtained slicing a double cone with a plane. (parabola, circle, hyperbola, and ellipse)
Conjecture Conclusion reached in a math statement using reasoning. Also known as an educated guess, which sometimes may be wrong.
Conjugates Binomials in the form a√(b) +c√(d) and  a√(b) +c√(d) for which a, b, c, and d are rational numbers.
Consecutive angles In a polygon consecutive angles share a common side.
Constant It is a number or value that remains always the same. Never changes.

10 is a constant.

Pi = 3.1416 is also a constant.

Constant Term The term in a polynomial that doesn’t have a variable factor.
Constraints The inequalities in a system of inequalities for which the graphs constitute the boundaries of the graph in the system's solution.
Construction A geometric figure drawn having as only tools a compass and a straight edge.
Continuous Function

If a function has a graph without a broken line then it is a continuous function.

Function whose graph is an unbroken

Continuously compounded interest formula The formula for calculating the continuously compounded interest is A=Pert.
Contrapositive In a conditional statement "if  p then q", the contrapositive is "if not p then not q", and always have the same truth value as the original conditional.
Converge For an infinite geometric series to converge it is necessary that |r|<1, where r is the common ratio  of the sequence in question.
Converse In a conditional statement "if p then q", the converse is "if q then p"
Convex polygon A polygon that doesn’t have diagonals containing points outside the polygon.
Coordinate The distance from the origin to a point in the number line.
Coordinate of a point

On a number line is the distance from the origin to the location of a point not in the origin.

On the coordinate plane is the pair (x, y) that determines the location of a point.

Coordinate proof A statement to be proven by means of using the coordinate plane in the process.
Coordinate space All the points (x,y,z) contained in the 8 octants generated by perpendicular number lines that form the x-axis, y-axis and z-axis in coordinate geometry that includes points in the space.
Coordinate Plane Defined by two number lines that are perpendicular and for which the intersection point is the origin (0,0); and the horizontal axis is the x-axis and the vertical axis is the y-axis.
Coplanar Points and lines that lie in the same plane
Corresponding angles Angles that occupy the same position in relation to geometric figures.
Corresponding parts Sides and angles in a polygon than have the same location in reference to each other.
Corollary Given a theorem, any statement that follows directly from this.
Cosine Ratio  determined by the hypotenuse in a right triangle and a side adjacent to a reference angle.
Counting Principle If event X may occur in x different ways and is followed by event Y that may also occur in y ways, then the event X followed by the event Y can occur in (x)(y) different ways.
Counterexample A particular instance that makes one statement false.
Co-vertices The co-vertices are located at the endpoints of the minor axis in the ellipse.
CPCTC Abbreviation for "Corresponding Parts of Congruent Triangles are Congruent."
Cross section It is the intersection of a solid object and a plane.
Cross-product property The product of the extremes in a proportion is equal to the product of the means.
Cubic Equation

Equation of the form
ax3 + bx2 + cx + d = y, where a, b, c, and d are real numbers and a is different from zero.

Largest exponent is 3

7x3 – 6x2 – 9x + 1 = y
Cumulative probability Putting together the probability over a continuous range of events is cumulative probability.
Cylinder A 3-D figure with two congruent circular bases that lie in planes that are parallel. The height (altitude) of the cylinder is the perpendicular distance between the planes containing the bases. In a right cone the altitude goes from center to center in the bases. In an oblique cylinder the segment that joins the centers of the bases is an oblique line (not perpendicular). Click at the figure for the surface area and volume formulas.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z  TOP