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AAS Congruence

Angle-angle-side congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure.

Abscissa

The horizontal axis, or the first coordinate in an ordered pair.

Acute Angle

An angle whose measure is less than 90 degrees.

Acute Triangle

A triangle whose interior angles are each acute, that is, less than 90 degrees (or ?/2 radians).

Adjacent

Next to each other. The idea is especially important in geometry, as with adjacent angles that share a common ray.

Adjacent Angles

Next to each other. Adjacent angles share a common ray and subsequently have a common vertex.

Alternate Exterior Angles

Given two parallel lines cut by a transversal, angles exterior to the parallel lines and on opposite (alternate) sides of the transversal are congruent.

Alternate Interior Angles

Given two parallel lines cut by a transversal, angles interior to (between) the parallel lines and on opposite (alternate) sides of the transversal are congruent.

Altitude

Height. The perpendicular or orthogonal distance above a fixed reference, as height above mean sea level. In geometry, the shortest distance from the base of an object to its apex (or top).

Altitude of a Cone

The shortest line segment from the apex (tip) of a cone to the plane of its base.

Altitude of a Cylinder

The distance between the planes containing the bases of a cylinder.

Altitude of a Parellelogram

The distance between opposite sides of a parallelogram

Altitude of a Prism

The length of the shortest line segment between the planes containing the bases of a prism.

Altitude of a Trapezoid

The distance between bases of a trapezoid.

Altitude of a Triangle

The shortest line segment between the vertex of a triangle and line containing the opposide of the triangle. The three altitudes of a triangle are concurrent at the orthocenter.

Amplitude

Periodic functions have an amplitude that is half the range between the highest and lowest values. The height a sinewave climbs from zero (if zero is its mean values) is its amplitude.

Analytic Geometry

Effectively coordinate geometry. It is the use of coordinates (in two or more dimensions) to determine geometric relationships.

Angle

The separation of two rays measured as the rotation of one of the rays. Usually measured in either degrees or radians, other systems of measuring rotation are also used to assign values to angles.

Angle Bisector

A ray (or line) that divides an angle into two congruent halves. The three angle bisectors of a triangle are concurrent at the incenter.

Angle of Depression

The angle below a horizontal reference. Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).

Angle of Elevation

The angle above a horizontal reference. Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).

Annulus

The area, or region, between two concentric circles of different radii.

Apex

The top. Most generally a singular situation as a point. The vertex of a cone or pyramid is an apex.

Apothem

The apothem applies to a regular polygon; it is either the distance from the center to a midpoint of a side, or the radius of an inscribed circle in the polygon.

Arc

A section of circumference. An arc is measured either by its own length or with a central angle.

Arc Length

A curved length; it can be the distance around a portion of a circle, or around a different shape of curved figure.

Area

The measure of a plane region defined to be within some boundary.

Area of a Circle

The extent of surface contained within the circle; ? times the square of the radius.

Area of a Kite

Half the product of the diagonals.

Area of a Parallelogram

Akin to the area of a rectangle, the area of a parallelogram can be expressed as the product of length times width.

Area of a Rectangle

The extent of surface contained within the rectangle; length times width.

Area of a Regular Polygon

One-half the product of perimeter times the apothem. Remember that regular means equilateral and equiangular.

Area of a Rhombus

If s is the length of a side and h is the height, s-squared times the sine of the big interior angle; s-squared times the sine of the smaller interior angle; half the product of the diagonals.

Area of a Sector of a Circle

It is the surface area of a slice of pie. We like arc length s=r?. So area of a sector is r-squared times theta all over two (? in radians).

Area of a Segment of a Circle

Given central angle theta, area of the segment is one-half the square of the radius times the quantity (? minus sine ?), provided ? is in radians.

Area of a Trapezoid

One-half the (sum of the bases) times the height. Or, the product of (median) and (altitude).

Area of a Triangle

One-half times the base times the height. Also, given perimeter a+b+c, and semiperimeter s=half that sum, then area = the square root of [s times (s-a) times (s-b) times (s-c)]. (Heron).

Area of an Ellipse

If 2a and 2b are the lengths of the major and minor axes of the ellipse, then the area of the ellipse is simply ?ab.

Area of an Equilateral Triangle

Given side of length s, the area of an equilateral triangle is s-squared times the-square-root-of-three over four.

ASA Congruence

Angle-side-angle congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure.

Axiom

Accepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact.

Axis

In physics, a line about which a body rotates. In mathematics, a line that divides a plane or space into two equal halves, typically demarcated in units.

Axis of Rotation

A line about which a body rotates.

Axis of Symmetry

A line about which a graph or body is symmetrical, that is, a mirror image on one side of the axis from the body or graph on the other side.

Base, Geometric

For a polygon, the line segment on the bottom. For a solid, the area of the "floor."

Bisect

Infinite lengths are not bisected. We bisect, or divide into equal halves, angles or line segments. Rays and lines are not bisected.

Bisector

A bisector cuts a geometric entity into two equal halves. It may divide an angle or a line segment, depending on the specific circumstance. A perpendicular bisector divides a line segment at a right angle.

Cardioid

A heart-shaped curve formed by rotating a circle and graphing the movement of that point as the "outside" circle traces around the inside circle.

Cartesian Coordinates

The familiar x-y coordinate plane is called the plane of Cartesian Coordinates; it is named for Rene Descartes.

Cartesian Plane

The Cartesian Plane contains the familiar x-axis and y-axis in which we plot ordered pairs. It is the familiar Rectangular Coordinate system.

Center of Mass

The Center of Mass of an object is the point at which forces acting on the object may be considered to be balanced or concentrated. In a triangle it is at the centroid, the point of concurrence where the medians of the triangle meet.

Center of Rotation

A point around which the rest of a body or object rotates is termed the Center of Rotation.

Center of Rotation 2

The point around which an object revolves or rotates is called the Center of Rotation.

Central Angle

A Central Angle is formed at the center of a circle. Think of the angle formed by cutting a slice of pie or cake from the center of a round baked good.

Centroid

The Center of Mass of a triangle (made from some flat material) is its Centroid. It is the point at which the medians of the triangles intersect, also called the point of concurrence.

Chord

A line (line segment) across a circle that does not pass through the center of the circle is termed a Chord.

Circular Cone

A Circular Cone need not have its apex directly above the center of its base.

Circular Cylinder

A Circular Cylinder does not have to have sides perpendicular to its base; its side may be oblique.

Circumcenter

The center of a circumscribed circle is called its Circumcenter. All regular polygons have a circumcenter, but most polygons do not. All triangles have a circumcenter.

Circumcircle

Also called the Circumscribed Circle, the Circumcircle encompasses a polygon and all vertices of the polygon are on the circle.

Circumference

The distance around a circle is its Circumference. It is the product of pi times the diameter, or twice the product of pi and the radius of the circle.

Circumscribed Circle

A circle around a polygon that contains all the vertices of that polygon is termed a Circumscribed Circle, also called a Circumcircle.

Clockwise

Rotation in the same direction as the hands of a traditional clock.

Collinear

Lined up perfectly; exactly aligned. In the same line are collinear points.

Complement of an Angle

Complementary Angles sum to 90 degrees or pi/2 radians. So the complement of an angle with measure x is (90 - x) degrees or (pi/2 - x) radians.

Complementary Angles

Complementary Angles sum to 90 degrees or pi/2 radians.

Concave

Bending inward or with an indentation. The opposite of convex, Concave applies to physical objects such as lenses or mirrors, as well as to polygons or solids.

Concave Polygon

A Concave Polygon has an "indentation." In moving around the perimeter of the polygon, at least one interior angle will be greater than 180 degrees.

Concenric Circles

Circles having the same centers but different radii are termed Concentric Circles.

Concentric

Literally having the same center point; centered at the same point.

Conclusion

When mathematical conclusions are valid the laws of math and science have been adhered to, and a logical approach has been taken. Sometimes conclusions are invalid because scientific or mathematic rigor has not been adhered to. Reason and judgment are often important to reaching sound or valid conclusions.

Concurrent

At the same point. Concurrent geometric entities occupy the same place, the same space.

Cone

A Cone is a geometric shape where a simple closed curve is connected to an apex (a point) with smooth lateral sides.

Congruence Test

There are various tests for congruence, which is the state of having identical size and shape.

Conic Section

Any of the various geometric entities that are formed by slicing a cone (or double cone) are termed Conic Sections. The list includes: circles, ellipses, parabolas, and hyperbolas.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the two angles formed on one side of the transversal between the parallel lines are termed Consecutive Interior Angles; they are supplementary.

Contraction

Contraction is the process by which some object or entity is shrunk or diminished in size or extent. It may be diminished in one dimension, or reduced proportionally if it is a two- or three-dimensional object. A Contraction can also be the result of such a process.

Contrapositive

Given a conditional statement, its Contrapositive is logically equivalent and is obtained by negating the original hypothesis and conclusion as well as reversing their order.

Converse

Given a conditional statement, as "If A, then B," the Converse results from switching the order of the hypothesis and conclusion: "If B, then A." The Converse may or may not be true given a true original statement.

Convex

When a geometric or physical entity has no indentations. Or, when a polygon has the property where no line segment across it leaves the interior of the polygon, the polygon is said to be Convex.

Coordinate

A value associated with the location of a point is a Coordinate. In one dimension a Coordinate is a single value. In two dimensions, a point is defined by two Coordinates as an ordered pair.

Coordinate Geometry

This branch of mathematics is a combination of algebra and geometry; it is analytic geometry.

Coordinate Plane

Two-dimensional entities are graphed or plotted in a plane, such as the rectangular plane or Cartesian Plane. Two-dimensional polar coordinates are also plotted in a plane. It requires an ordered pair to specify a location in a plane.

Coplanar

In the same plane; of the same plane. Most generally, points within the same plane are said to be Coplanar.

Corollary

A Corollary is like a baby theorem.

Corresponding Angles

Sometimes Corresponding Angles refer to the "same" angle in two similar (or congruent) polygons. Or, when parallel lines are cut by a transversal, Corresponding Angles are "on the same corner of the intersections."

Coterminal

When one angle is in the same position as another, as adding or subtracting 360 degrees or 2 pi radians puts a rotating angle in the same position as the previous angle, we say the angles are Coterminal.

Counterclockwise

For angles in standard position, we use a Counterclockwise rotation for positive measurement of the angle's rotation. This is the direction opposite the traditional movement of analog clock hands.

CPCTC

In geometry class we use this shorthand for "Corresponding Parts of Congruent Triangles are Congruent."

Cross Product

A product of vectors that generates another vector is often a Cross Product.

Cube

A six-sided orthogonal box with square faces; a right square parallelepiped. The result of raising a real value to its third power. The process of multiplying a number times itself and times itself again.

Curve

Beware that mathematicians consider straight lines to be Curves!

Cycloid

The path that a point on the outside of a rolling wheel makes is termed a Cycloid.

Cylinder

A Cylinder may or may not have circular bases. The lateral sides are connected with congruent, parallel bases that may be the shape of any closed curve.

Decagon

A 10-sided polygon is called a decagon.

Deductive Logic

Deductive Logic is employed before events have transpired, before the fact.

Degree, Angle

One 360th of a full rotation is an angle of one degree.

Diagonal

Convex polygons have Diagonals from each vertex to each non-adjoining vertex.

Dilation

To grow in size is to dilate, or to undergo Dilation. Most often it means to increase proportionally in all dimensions, but not strictly. Sometimes Dilation is expansion in one dimension only.

Dimension

A line has one Dimension. A plane has two Dimensions. A three-dimensional object occupies space.

Directrix

A line specific to conic sections hyperbolas, parabolas, and ellipses, known as a Directrix, serves to describe along with the location of the focus (or foci) the loci (points) on the graph of the function.

Disk

A Disk is most often a circular object with a relatively thin measure in the direction orthogonal to the plane of the circular bases.

Distance

A length from one point to another is considered a Distance. Any measurement in one dimension confers a length, which is Distance.

Dodecagon

A 12-sided polygon is a Decagon.

Dodecahedron

A 12-faced polyhedron is called a Dodecahedron.

Ellipsoid

Think of a blimp (a zeppelin) or a football (American football).

Equiangular

Having all angles of equal measure is to be Equiangular. Equilateral polygons are most often (but not necessarily) also equiangular; they are termed Regular Polygons.

Equidistant

Literally of the same distance to some reference point is the essence of Equidistant.

Equilateral

Polygons with all sides congruent are said to be Equilateral. Most Equilateral polygons are also equiangular (but not necessarily). Polygons that are both equilateral and equiangular are termed Regular Polygons.

Equivalence

When we establish Equivalence we set forth two or more equivalent or equal entities.

Euclidean Geometry

The plane geometry we all study in school is a form of Euclidean Geometry, spiced with a few three-dimensional figures for flavor.

Exterior Angle

An Exterior Angle is most commonly the angle formed between the extension of a side of a polygon and the adjoining side.

Face, Geometry

Solids, in geometry, are considered to have faces when lateral sides are flat, that is, planar.

Foci

Certain points in conic sections (and other geometric entities) are termed Foci, the plural of focus. They are important to the mathematical mechanics of the functions.

Focus

A specific point in a conic section (or other geometric entity) is termed a Focus, the singular form of the word foci. They are important to the mathematical mechanics of the functions.

Formula

A recipe or algorithm for calculation, evaluation, simplification, or just about anything we do in mathematics can be called a Formula.

Fractal

Certain shapes maintain their shape through all permutations of multiplication, growth, dilation, division, contraction, or shrinkage. Such shapes are Fractals.

Frustum

Slice a pyramid (or cone) parallel to its base, remove the top. What remains under the "missing top" is the Frustum.

Geometric Mean

The Geometric Mean of two real values is the square root of the product of the two values. More generally, the Geometric Mean of n values is the nth root of the product of the n values.

Great Circle

Basically, any circle that resides on a sphere is a Great Circle.

Greek

Anyone interested in learning mathematics should embrace the Greek alphabet with 24 letters from alpha to omega.

Heading

Quite similar to bearing, Heading is a dynamic direction that implies motion.

Height

Altitude. How tall something is, measured in some perpendicular fashion to the "bottom" is its height.

Helix

A straight line wrapped around a circular cylinder at some angle not perpendicular to the base of the cylinder results in a Helix.

Heptagon

A seven-sided polygon is a Heptagon; also called a septagon.

Heron's Formula

A wonderful little recipe (algorithm) for finding the area of a triangle when sides are known and the altitude is not known, the formula is best expressed with a semiperimeter.

Hexahedron

A six-faced polyhedron is termed a Hexahedron.

Horizontal

Horizontal comes from orientation like the horizon; parallel to the "flat" surface of the earth; perpendicular to vertical.

Hyperbola

A conic section of specific mathematical relation to foci; its shape is the intersection of a double cone with a plane. The difference between distances from a locus on the Hyperbola to the two foci is a constant.

Hyperbolic Geometry

Hyperbolic Geometry is non-Euclidean geometry; within it the Parallel Postulate does not hold.

Hypotenuse

The longest side of a right triangle is the Hypotenuse; it is always opposite the 90-degree angle (or right vertex).

Hypothesis

In a biconditional statement the hypothesis is followed by a conclusion. In the scientific method, the hypothesis is the conjecture to be proved or disproved.

Identity

As opposed to a conditional statement that is sometimes true, an Identity will always be true. The multiplicative identity is 1; the additive identity is zero.

If-and-Only-If (Iff)

A statement that shows a condition both necessary and sufficient for the assertion.

If-Then Statement

The classic biconditional statement is often phrased as an If-Then proposition.

Impossibility

Despite what some "possibility thinkers" espouse, some things are mathematically impossible. For example, an exact real number cannot be simultaneously irrational and rational.

Incenter

The center of a circle inscribed within a polygon. For a triangle, it is the point of concurrence of the angle bisectors.

Incircle

A circle inscribed within a regular polygon (or any triangle) is an Incircle. In a regular polygon, the radius of the Incircle is the apothem.

Inductive Logic

Inductive Logic is the logic of after-the-fact, or a posteriori. It results from observation of transpired events.

Infinite

In common language, not countable in any practical manner. In math, having no bounds or boundary.

Infinite Geometric Progression

When a geometric progression has a common ratio less than one (technically, a common ratio whose absolute value is less than one), then the Infinite Geometric Progression will converge to a limit.

Infinitesimal

Infinitely small is Infinitesimal, so tiny that it occupies no space. While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size.

Infinity

That without bound; limitless.

Initial Side of an Angle

In standard position, the Initial Side of an Angle is the ray along the positive x-axis, from the origin.

Inscribed Angle

An angle inside a circle with its vertex on the circle is an Inscribed Angle.

Inscribed Circle

This term is the same as Incircle, a circle inscribed within a polygon.

Interior

Interior means within or "in-between."

Interior Angle

Any angle inside a geometric entity, or between geometric lines, is considered an Interior Angle.

Intersection

Where geometric entities cross, or where sets have common elements, is termed an Intersection.

Interval

The space or region between two defined values is an Interval.

Interval Notation

With brackets or parentheses, depending on whether endpoints are included in the set, Interval Notation expresses the solution set for an inequality.

Invariant

Constant. Not changing. Static. That which does not vary.

Inverse

Inverse carries a lot of meanings within the language of mathematics.

Inverse Trigonometric Function

Given a number, this function returns the angle whose trig function is the given number.

Inverse, Conditional

Given an initial if-then statement, the negative of both the hypothesis and conclusion provides the Inverse to the original statement.

Iota

The ninth letter of the Greek alphabet, Iota means a very small amount.

Irrational Number

An Irrational Number cannot be expressed exactly as the ratio of two integers. Irrational Numbers, when expressed as decimals, never repeat or terminate.

Isosceles Trapezoid

A trapezoid (quadrilateral with one pair of parallel sides) whose non-parallel sides are congruent is termed an Isosceles Trapezoid.

Isosceles Triangle

A triangle with two congruent sides.

Kappa

The tenth letter of the Greek alphabet is Kappa, popular on college campuses with sororities and fraternities.

Kite

A quadrilateral with two pairs of congruent sides, and unlike, say, a parallelogram, the congruent sides of a kite are adjacent. Its diagonals meet at right angles.

Lateral

The flat sides of a geometric solid are generally termed the Lateral sides or Lateral surface area.

Lateral Surface Area

The Lateral Surface Area of a geometric solid is the expanse of the flat sides (or smooth sides). Be careful, some solids have faces that are termed bases and not lateral surfaces.

Leg, Trapezoid

The Leg of a Trapezoid is one of the non-parallel sides.

Leg, Triangle

Most generally the legs of a triangle refer to the perpendicular sides of a right triangle only.

Lemma

A little, inconsequential theorem is sometimes called a Lemma.

Line

A collection of points that comprise the shortest path between two points in Euclidean geometry is a Line; all points in a Line are collinear and, of course, coplanar.

Line Segment

A section of a line, with endpoints on both ends, is a Line Segment.

Linear

As the first four letters imply, Linear means "of a line" or "lined up" in a collinear fashion.

Linear Pair

Two adjacent supplementary angles form a Linear Pair.

Loci

The points that comprise a function (or graph thereof) are its Loci.

Locus

A single point on a function or on its graph is a Locus.

Logic

Logic takes many forms and is instrumental in understanding the language of mathematics.

Magnitude, Powers of Ten

Often when we compare the multiplication by various powers of ten we speak of the magnitude of the effect of the multiplication.

Major Axis

Certain conic sections have a Major Axis, a line (segment) between vertices.

Measure

A noun or verb, Measure implies comparison to an established standard.

Measurement

The result from comparison to an established standard, Measurement may be exact only to an agreed-to precision.

Median, Trapezoid

The average of the lengths of the bases of a trapezoid. The Median is a line segment parallel to and equidistant from the bases.

Median, Triangle

A triangle has three Medians, each a line segment from a vertex to the midpoint of the opposite side of the triangle. Medians are concurrent at the centroid.

Midpoint

Every line segment (or side of a polygon) contains a point equidistant from the endpoints (or vertices), the Midpoint.

Minimize

A process to establish the least extent, value, or size possible.

Minor Axis

A line or line segment specific to certain conic sections.

Minute, Angle

For angles, one Minute is one-sixtieth of a degree. One Minute is equivalent to 1/21600 of a circular rotation.

Mode

While Mode can take on several meanings in mathematics, it generally is used for the value of data with the greatest frequency of occurrence in a list of values.

Modus Ponens

We have "If A, then B." Modus Ponens is a piece of logic that goes like this: if we know A to be true, then we know that B must be true, too.

Modus Tollens

Begin with "If A, then B." That's a given. We (somehow) know that B is false. We then may infer (but not conclude) that A is false. Modus Tollens is not particularly robust; it is not entirely dependable.

Multiplicative Inverse

Another name for Multiplicative Inverse is reciprocal. Reciprocals multiply to one.

N-gon

When a polynomial has so many sides that we cannot easily remember its name, we just take the number of sides (n) and add "gon" to our characterization, as a 16-sided polygon would be called a "16-gon."

Natural Numbers

The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... More precisely in the language of math these are the positive integers.

Negative

Real values less than zero are Negative. We also consider the Negative of a real value to have the opposite sign, as the opposite (or Negative) of a Negative value is positive.

Negative Reciprocal

The product of two Negative Reciprocals is -1. When lines in Cartesian or rectangular coordinates meet at right angles they have Negative Reciprocal slopes, unless they are precisely horizontal and vertical.

Non-collinear

Not linear, not aligned, not part of the same line. Not collinear.

Non-Euclidean

A geometry in which the Parallel Postulate does not hold may be termed a Non-Euclidean geometry. In such a geometry, the shortest distance between two points may not be a straight line.

Nonagon

A nine-sided polygon.

Nonnegative

We have occasions to refer to all positive values as well as to zero. These are all the real values that are Nonnegative. Literally, not negative.

Nth Root

Given some integer N and a real value, the Nth Root of the real value is the number that when raised to the N power returns the real value.

Null Set

The Null Set is the empty set. Mathematically there is but one empty set, the unique Null Set, the set with nothing in it.

Number Line

The real Number Line is a depiction of the set of all real numbers from negative infinity to positive infinity. All real numbers lie on the Real Number Line.

Oblique

In one sense, at an angle or not perfectly horizontal or vertical. An Oblique triangle is any triangle that is not a right triangle.

Obtuse

In common language Obtuse means obscure and confusing, obfuscatory. An Obtuse angle measures more than 90 degrees (and less than 180 degrees).

Octagon

An eight-sided polygon.

Octant

As we have four quadrants in the rectangular plane, we have eight Octants in rectangular space. In three dimensions the three axes divide space into eight sections, each termed an Octant.

Odds

The likelihood or probability of an event or specific outcome is termed the Odds of the event occurring. Odds, or probabilities, are always represented with values between 0 and 1, or between zero and 100 percent (inclusively).

Omega

The last, or 24th, letter of the Greek alphabet is Omega. Upper-case Omega is used for ohms, a unit of electrical resistance. Lower-case Omega is used for angular velocity, a speed of rotation.

One-Dimensional

Linear, or along one line of direction. Informally, constrained to stay along a narrow line.

Opposite

Many meanings are found for Opposite, including having direction 180 degrees from an original direction, or having the negative sign of a previous sign. Opposite real values have identical absolute values.

Ordered Pair

Two coordinates are required to label a point in a plane, typically (x, y).

Ordered Triple

Three coordinates are required to label a point in space, typically (x, y, z).

Origin

In one dimension: (0). In two dimensions: (0,0). In three dimensions: (0, 0, 0).

Orthocenter

The Orthocenter of a triangle is the point of concurrence of the altitudes of the triangle.

Orthogonal

Most generally Orthogonal means perpendicular to a plane.

Oval

In common language, any elliptical shape or not-quite round "circular" shape is called an Oval. Mathematically, an ellipse is not an Oval.

Parabola

The graph of a quadratic function is a Parabola, a conic section.

Parallel Lines

Coplanar Lines that never meet or cross are Parallel. If lines simply never cross, they may be skew (non-coplanar).

Parallel Planes

Two distinct planes, collections of flat expansion of points, that never meet are considered Parallel Planes.

Parallel Postulate

Given a line and a specific point not on the line, there is only one line through the specific point parallel to the given line.

Parallelepiped

A shoebox is a Parallelepiped. Any geometric body with six faces that are each parallelograms that are in planes parallel to the opposite face.

Parallelogram

A quadrilateral with two pairs of parallel sides is a Parallelogram; it has many dependable properties.

Perfect Square

Most generally a Perfect Square is an integer that is the product of another integer times itself.

Perimeter

The distance around the outside of a planar object or a plane figure is its perimeter.

Perpendicular

At right angles.

Perpendicular Bisector

A line segment (or side of a polygon) has a unique line through its midpoint perpendicular to the line segment (or side).

Pi

The constant ratio of circumference to diameter is represented by the 16th letter of the Greek alphabet; it is approximately 3.14159.

Plane

An infinite expanse of points in two dimensions.

Plane Geometry

Basic geometry is Plane Geometry. We hold to the parallel postulate and Euclidean principles.

Point

A location of infinitesimal size, that is, no size. A mathematical idea.

Polygon

A closed plane figure with straight sides.

Polyhedron

A geometric solid with faces that are polygons.

Postulate

A far-reaching conjecture or sense of reasoning for which an obvious and substantive base appears most reasonable.

Precision

The quality of finer measurement or estimation is termed Precision.

Prism

A Prism is a geometric solid with two congruent polygons within parallel bases connected by faces that are parallelograms.

Proof

An ingredient in pudding.

Proper Subset

A set that is a subset of a given set and not identical to the given set is a Proper Subset of the given set.

Proportional

In a (constant) ratio.

Psi

The 23rd letter (next-to-last) of the Greek alphabet.

Pyramid

A geometric solid with a base of a polygon and planar lateral sides that meet at a point called an apex is termed a Pyramid.

Pythagorean Identities

sin^{2}x + cos^{2}x = 1; 1 + tan^{2}x = sec^{2}x; 1 + cot^{2}x = csc^{2}x

Pythagorean Triple

A series of three integers for whom the Pythagorean relation holds, as 3-4-5 or 5-12-13, because 3^{2} + 4^{2} = 5^{2} and 5^{2} + 12^{2} = 13^{2}.

Quadrangle

Another name for a quadrilateral, a four-sided polygon.

Quotient

The result of the operation of division, the Quotient results from dividing a dividend by a divisor; also the value of a fraction that is always numerator divided by denominator.

Radical

A root symbol or the root itself is sometimes termed a Radical.

Radicand

A number taken to a root is a Radicand; the number under a root sign.

Radius

One-half the diameter of a circle is the Radius. It is the distance from the center of a circle to any point on the circle.

Ratio

Sometimes Ratio is meant to state a constant proportion. More generally, the Ratio of two real values is the quotient of one number divided by the other.

Ray

A set of collinear points, a Ray has an endpoint and proceeds infinitely far in a single direction.

Rectangle

A quadrilateral with many special properties, including all those of a parallelogram, and then some.

Reflexive

Literally "in relation to itself." When we say A = A, we employ a Reflexive property.

Regular Polygon

A Regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent).

Regular Polyhedron

A geometric solid with all faces regular polygons.

Regular Prism

A Prism with bases of Regular polygons.

Regular Pyramid

A Pyramid with a base of a Regular polygon.

Regular Right Prism

A Prism with bases of Regular polygons and lateral faces perpendicular to those bases.

Regular Right Pyramid

A Pyramid with a Regular polygon for a base and an apex directly above the center of the base.

Revolutions Per Minute

Abbreviated "rpm" it conveys the number of complete circular rotations that occur every 60 seconds at some constant rate of revolution.

Rho

Lower-case Rho, the 17th letter of the Greek alphabet, is often used for density (mass per unit volume) in physics.

Rhombus

A quadrilateral with four congruent sides. Its diagonals are perpendicular.

Right Angle

An angle of 90 degrees or pi/2 radians. Perpendicular lines meet at Right Angles.

Right Circular Cone

A cone with a circular base and an apex directly above the center of the base.

Right Circular Cylinder

A circular cylinder with sides orthogonal to parallel bases.

Right Cone

Any Cone, circular or otherwise, with its apex directly above the center of the base.

Right Cylinder

Any Cylinder, circular or otherwise, with lateral sides orthogonal to the bases.

Right Prism

A Prism with lateral sides orthogonal to the bases.

Right Pyramid

A Pyramid with its apex directly above the center of the base.

Right Regular Prism

A Prism with bases of Regular polygons and lateral faces perpendicular to the bases.

Right Regular Pyramid

A Pyramid with a Regular polygon for a base and an apex directly above the center of the base.

Right Square Parallelepiped

Cube.

Right Square Prism

A cube, or a shoebox if the ends of the shoebox are square.

Right Triangle

A triangle with a right angle.

Rotation

Movement in a circulation or circular fashion, often around a point or an axis, is termed Rotation.

SAA Congruence

Side-Angle-Angle Congruence establishes two congruent triangles.

SAS Congruence

Side-Angle-Side Congruence establishes Congruence between two triangles.

SAS Similarity

Side-Angle-Side Similarity employs a fixed ratio between pairs of sides of triangles.

Scalene

A triangle is considered Scalene if no two sides have the same length.

Secant

The term applies to either a line containing the chord of a circle (or some other line segment between points on a function), or one of the six basic functions in trigonometry, the cofunction of the cosecant and the reciprocal of the cosine.

Second, Degree

While "second degree" applies to a polynomial, a single Second with respect to Degree measure is one-sixtieth of one minute, or one sixtieth of one sixtieth of one degree, or 1/1,296,000 of a revolution.

Second, Time

One sixtieth of a minute, or 1/3600 of an hour, is one Second of Time.

Sector

A piece of a circle bounded by a central angle.

Segment, Circle

A portion of a circle bounded by a chord and the circle itself.

Segment, Line

A Line Segment is a set of collinear points bounded on both ends with, literally, endpoints.

Semicircle

Half a circle; the portion of a circle on one side of a diameter.

Set

Any collection of objects or values is considered a Set, whose cardinal number is the number of objects in the Set.

Set Union

The Union of two (or more) Sets is the Set that contains both (or all) Sets. Logically, the Union of two Sets A and B is the Set of elements contained in either Set A or B, literally "A or B."

Similar

Geometrically, figures of like shape and proportions are said to be Similar.

Similarity

Literally the quality of being Similar, which is to have the same shape and proportions, but not necessarily of the same size.

Simple Closed Curve

A planar figure that neither crosses itself or contains a gap is a Simple Closed Curve; note that a curve can be "straight" according to the mathematicians.

Simple Harmonic Motion

Periodic Motion with constant length of cycle time (a fixed period) is termed Simple Harmonic Motion.

Sine

One of the six basic trig functions, in a right triangle the Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Sinusoid

A sine wave is called a Sinusoid; a cosine graph is also a Sinusoid.

Skew

Lines neither intersecting nor parallel (non-coplanar lines) are termed Skew lines.

Slope

A number associated with a line graphed in a plane, Slope is the ratio of rise over run, an indication of the steepness of the line. We may write a line as y = mx + b and use the value of m for Slope.

Slope-Intercept Equation of a Line

The familiar y = mx + b, where m represents Slope and b is the y-Intercept.

SOHCAHTOA

A mnemonic device for remembering: sine-opposite-hypotenuse; cosine-adjacent-hypotenuse; tangent-opposite-adjacent. Also stands for "some old hippie caught another hippie tripping on acid."

Solid

A three-dimensional geometric figure or body that includes the interior region.

Solution

Too often in math class, "the answer." More directly, a Solution is a value (or set of values) that makes a mathematical statement true.

Speed

A (typically fixed) ratio of length or distance to a unit of time; Speed is a scalar value, as in miles per hour (mph) or feet per second (fps).

Sphere

A three-dimensional figure comprised of points equidistant from a center point; a Sphere has a fixed radius.

Spherical Geometry

Unlike plane Geometry, Spherical Geometry is not based on the parallel postulate. Many of our accepted geometric theorems, principles, and tenets (from plane Geometry) simply do not hold in Spherical Geometry.

Spheroid

An oblate sphere. Sometimes, an ellipsoid.

Spiral

Sometimes Spiral is used to describe a helix. A genuine Spiral is a plane figure of changing radius from a (usually fixed) origin.

Square

One noun: the regular quadrilateral, equilateral and equiangular. Another noun: the result of multiplying a number times itself. Or, the verb: the operation of multiplying a number times itself, equivalently raising it to power two.

Square Root

Given a real value, the number that times itself (squared) produces the given value is its Square Root

SSA Ambiguity

Side-Side-Angle congruence is not enough to establish congruence between two triangles; it is the Ambiguous case.

SSS Congruence

Two triangles whose corresponding sides are congruent are themselves congruent.

SSS Similarity

When corresponding sides of two triangles are in a fixed ratio the triangles are similar.

Standard Position

An angle in Standard Position has been rotated counterclockwise (for positive rotation) from an initial ray on the positive x-axis.

Straight Angle

An angle of 180 degrees or pi radians.

Supplementary

Supplementary angles sum to 180 degrees, or pi radians.

Symmetry

Having a like but reversed profile or image (a mirror image) about a line is having the quality of Symmetry about the axis (of Symmetry).

System of Equations

Most generally simultaneous Equations, or a set of Equations with identical variables.

Tangent

A line that touches a function curve at a single point is said to be Tangent to the function. Tangent is also one of the six basic trigonometric functions; it is the ratio of the opposite side (from a specified angle) of a right triangle to the adjacent side.

Tangent Line

A Line is said to be Tangent to a function when it touches the graph of the function at a single point.

Terminal Side of an Angle

When in standard position, an Angle has an initial side, a ray on the positive x-axis, and a Terminal Side where the rotation of the angle stops, at an angle of specific measure (in degrees or radians).

Tessellate

A planar pattern of repeating geometric shapes is a Tessellation; to produce these shapes is to Tessellate.

Tetrahedron

A polyhedron with four faces.

Theorem

A mathematical principle typically proved with some rigor is often a Theorem.

Theta

The eighth letter of the Greek alphabet is Theta, a common variable for an angle.

Three Dimensions

The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates.

Three-Dimensional Coordinates

Three-Dimensional Coordinates require an ordered triple to label a point in space.

Transitive Property

The Transitive Property is exhibited when three values are related in the following manner: If A = B and B = C, then A = C. The relation need not be equality.

Transversal

A line that crosses two or more parallel lines is often termed a Transversal.

Trapezium

In the United States, a quadrilateral with no parallel sides; in other English-speaking countries, what Americans term a trapezoid, a quadrilateral with one pair of parallel sides.

Trapezoid

A quadrilateral with one pair of parallel sides (U.S.); the same figure is a trapezium in some other English-speaking countries.

Triangle

A three-sided polygon. Triangles are either acute, right, or obtuse.

Triangulation

We may conduct geographic surveys or determine the altitude of various objects by a process termed Triangulation.

Trigonometric Identities

The various statements in Trigonometry that are universally true, typically for any angle in the statement, are called Trigonometric Identities. For example, sin²x + cos²x = 1 for any angle x.

Truncation

Replace the lesser digits of some number with zeros with no regard for rounding; this is Truncation.

Two Dimensions

A plane has Two Dimensions. Planar figures are Two Dimensional.

Uniform

Constant and unchanging; fixed.

Union

The Union of two or more sets is the set of elements from all the sets. The Union of sets A and B is literally the set "A and B."

Unit Circle

A Circle of radius one centered at the origin is termed the Unit Circle.

Vector

Often represented with an arrow, a Vector is a quantity with both magnitude (size) and direction.

Venn Diagram

Most often graphics of overlapping circles and ovals, a Venn Diagram depicts sets, subsets, and their intersections and unions.

Verify

To confirm is to Verify. When we Verify, we prove or establish some assertion to a dependable conclusion independent from bias. There is wisdom in these words: "Trust, but Verify."

Vertex

A "corner" of a polygon is a Vertex; an extremum of a conic section is a Vertex; the endpoint(s) of rays that form an angle is a Vertex.

Vertical Angles

When two lines cross (intersect) they form two pairs of Vertical Angles; the Angles within each pair of Vertical Angles are congruent.

Volume

The extent to which an object fills units of three-dimensional space is its Volume.

y-z Plane

In three dimensions, the plane orthogonal to the x-axis.

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