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If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality.

Someone that is in the field of pharmaceuticals would use this when making a new prescription drug

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Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.

Someone that is trying to solve for an equation would use this process

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a plane figure with four equal straight sides and four right angles.

someone that is making a computer would use squares for the keys

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In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Y=mx+b would be used by someone trying to make a ramp the right angle

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Combining like terms is a mathematical process used to simplify an expression or to add or subtract polynomials. Learn how to recognize like terms and combine them in this lesson, then check your knowledge with a quiz.

Someone trying to simplify an answer would use this

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In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle.

A chef would use this when splitting circular foods in half

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A chord of a circle divides the circle into two regions, which are called the segments of the circle.

This would be used by someone that is in the car rim business

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The segment addition postulate is a fairly obvious-seeming postulate which states that: If a point B lies on a line segment , then . That is, the distance from one endpoint to the other is the sum of the distances from the middle point to either endpoint.

Someone that is interested in making an even length of a telephone pole that needs an extention.

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a part or subdivision, esp of a society or an economy: the private sector

Someone that is cutting a cake would use this to make it evenenly cut

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A secant line is a straight line joining two points on a function

This would be used by someone who analyzes statistics

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A scalene triangle is a triangle that has three unequal sides

Anyone that is teaching the basics of triangles would have to explain this type

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A scale factor is a number which scales, or multiplies, some quantity

Someone that is scaling an artwork would use this to make it more accurate

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the action of rotating around an axis or center.

A car designer would use this to make sure the wheels are spinning the right way

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A rigid motion is the action of taking an object and moving it to a different location without altering its shape or size

Someone animating would need this for making different motion occur

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In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line.

Someone that is trying to make a skateboard ramp would need to know how to make a right angle from different lines.

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a rhombus(◊), plural rhombi or rhombuses, is a simple (non-self-intersecting) quadrilateral all of whose four sides have the same length.

Someone designing the wooden shapes that you would use in elementary school would need to know how to make this shape

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a rectangle is any quadrilateral with four right angles

A designer of furniture would use these to make up their different designs

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the radius of a circle or sphere is the length of a line segment from its center to its perimeter

Anyone who makes sports balls, would need this to make their products accurate.

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a previous statement or proposition from which another is inferred or follows as a conclusion.

A lawyer would use this when stating their case and backing it up

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A parallelogram is a quadrilateral with opposite sides parallel

An architect would use this when they are designing a building that needs a sturdy base

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In geometry, parallel lines are lines in a plane which do not meet;

A railroad engineer would use this to make sure the tracks are even

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the absence or opposite of something actual or positive.

This would be used by a jury in a court

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A linear pair is a pair of adjacent angles formed when two lines intersect. In the figure, 1 and 2 form a linear pair. So do 2 and 3, 3 and 4, and 1 and 4. The two angles of a linear pair are always supplementary, which means their measures add up to 180o.

This would be used by someone trying to make a ramp

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An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle

this would be used when making wheel spokes

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Conditional elimination is the name of a valid rule of propositional logic.

This would be used by someone that is trying to find a solution

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In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, or simplification) is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.

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https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/220px-Venn_0000_0001.svg.png

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Conditional elimination is the name of a valid rule of inference of propositional logic.

It would be used by someone trying to figure out what to do on a math problem/ a tutor teaching their student what to do

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A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion.

This is used by lawyers when trying to counter points

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the middle point of a circle or sphere, equidistant from every point on the circumference or surface.

Someone that is making an ice rink would use this to know where to put the circles

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The angle addition postulate states that if B is in the interior of AOC, then. That is, the measure of the larger angle is the sum of the measures of the two smaller ones.

Anyone that works with plowing in the winter would use this when adjusting the angle of their plow

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wolframalpha.com

searching terms on google.com

KhanAcademy.org

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The Zero Product Property simply states that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more of the factors is zero. This is particularly useful when solving quadratic equations.

Mathematicians would use this property in their professional work/ when teaching it to other people.

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each of the pairs of opposite angles made by two intersecting lines.

An architect would use these when trying to design a building/ structure

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a plane figure with three straight sides and three angles

Triangles are used by many professionals due to them being such a common shape/ polygon

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A 4-sided flat shape with straight sides that has a pair of opposite sides parallel.
A math teacher would likely use this term to explain a particular polygon that is pictured below.

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A 4-sided flat shape with straight sides and NO parallel sides

A math teacher would use this term to explain a shape where none of the sides are parallel with another.

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A transversal is two parallel lines intersected by a third line at an angle. The third line is referred to as the transversal line. When this happens several angles are created. You can use these angles to find the measurements of other angles.

A chef may use this term when talking about splitting something, but not having that thing be symmetrical

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A translation is a direct isometry. Definition: A translation (notation ) is a transformation of the plane that slides every point of a figure the same distance in the same direction.

A business professional may use this when dragging and dropping different things on the computer

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The following property: If a = b and b = c, then a = c. One of the equivalence properties of equality. Note: This is a property of equality and inequalities.

A student may use this when they are trying to double check their work

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A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation.
A graphic designer would use this term when they are mirroring/ reflecting certain shapes or objects.

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an angle of 180°.

A roller coaster designer would use this angle when designing a launched coaster

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A tangent line is a straight line that touches a function at only one point. (See above.) The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point

A designer of an advanced self balancing scooter would use this when making the product due to the picture below being so similar to the 'scooter'

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Mathwords: Symmetric Property of Equality. The following property: If if a = b then b = a. This is one of the equivalence properties of equality.

A mathematician would use this property when trying to find the inverse of a problem with a step that contains subtraction.

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Supplementary Angles. Two Angles are Supplementary when they add up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees.

A car company is likely to use this, they need to make sure that the angles they're using are precise. When they need there to be a 180 degree angle they will test it using this or a computer that in the end will have used this

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A triangle where one of the angles is equal to 90 degrees

A professional in the area of design would use right angles many times each and every day. They may not realize that they are, but the various shapes that they are using do contain triangles and more often than not... right triangles.

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Reflexive, Symmetric, Transitive, and Substitution Properties. The Reflexive Property states that for every real number x, x = x. The Symmetric Property states that for all real numbers x and y, if x = y, then y = x.

This property would be most likely used by those with an interest in perfecting their work

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

Anyone that looks into a mirror uses this transformation

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A ray is a part of a line that has one endpoint and extends in one direction without ending. A line segment is a part of a line between two endpoints. The figure extends in This figure has one opposite directions without endpoint and extends ending

An artist would use rays in their artwork when outlining/ setching.

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a four-sided figure.

A sculptor would use this polygon if they were to make a flatter bust or sculpture

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In Geometry, we define a point as a location and no size. A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions. There are three undefined terms in geometry.
Anybody that has a career in business and deals with tracking money spent would need to know of points in a database

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the numerical value of pi.

A mathematician would use pi when finding the area of a circle

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Put this together with the sign change, and you get that the slope of the perpendicular line is the "negative reciprocal" of the slope of the original line — and two lines with slopes that are negative reciprocals of each other are perpendicular to each other.

Someone that creates problems on KhanAcademy is likely to use this property when making problems that have to do with slope/ slope intercept form

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Adjective Intersecting at or forming a right angle or right angles. Noun A line or plane that is perpendicular to a given line or plane.

perpendicular lines are used by many people, but mainly those in the construction and math world

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the continuous line forming the boundary of a closed geometric figure.

A home-owner that wants to extend the size of a room would find the perimeter when they are seeing how big of a room they could fit next to another space in the home.

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a plane figure with five straight sides and five angles.

An architect would use this polygon when designing certain things such as the government building

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a plane figure with eight straight sides and eight angles.

An architect would use this polygon when designing certain things such as the stop sign pictured below

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An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A triangle must be either obtuse, acute, or right.

An architect would use this polygon when designing certain things such as a support for a bridge.

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An obtuse angle is one which is more than 90° but less than 180°

A professional in an industrial environment would use obtuse angles when making things like seating or supports

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a plane figure with nine straight sides and nine angles.

An architect would use this polygon when designing certain things like a problem for students in a math class

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The Multiplicative Identity Property. For a property with such a long name, it's really a simple math law. The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.

A math teacher would use this property when they are trying to make life hard for their students

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The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal (i.e. equality is preserved).

Mathematicians would use this property when trying to figure out a simpler question like that of a^2+b^2=c^2

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A minor arc (left figure) is an arc of a circle having measure less than or equal to ( radians).
a pie baker may want to combine flavors as a test and only put a small amount of one in the minor arc

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A major arc (right figure) is an arc of a circle having measure greater than or equal to ( radians).

a cake decorator may want to only cover part of the cake with a certain topping and would use this

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A line segment is a part of a line between two endpoints. The figure extends in This figure has one opposite directions without endpoint and extends ending.

An artist that is making realistic art with hatching would use line segments

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For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it.

An artist would use lines when they are making a rough sketch

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A quadrilateral is a kite if and only if any one of the following conditions is true: Two disjoint pairs of adjacent sides are equal (by definition). One diagonal is the perpendicular bisector of the other diagonal. (In the concave case it is the extension of one of the diagonals.)

A toy designer would use this polygon when designing child kites

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In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

An architect would use this polygon when designing certain things like the base shape of a vase without curves

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An intercepted arc is the arc that is formed when segments intersect portions of a circle and create arcs.These segments in effect 'intercept' parts of the circle. The picture below shows examples of intercepted arcs. Note: The examples below use chords to create the intercepted arc.

A student would use this when trying to find an intercept of a circle

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a plane figure with six straight sides and angles.

A web designer would use this polygon when designing certain things like the 9gag logo

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a plane figure with seven straight sides and angles.

An architect would use this polygon when designing certain things

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a plane figure with eleven straight sides and angles.

An architect would use this polygon when designing certain things

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An equiangular triangle is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always a third of that, or 60°

Someone that works at a pencil company would use this polygon when designing certain things like an eraser

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The three sides of any equilateral triangle are equal. The three angles of any equilateral triangle all measure 60 degrees.

An architect would use this polygon when designing certain things such as a roof to a church due to the angles being the same as one another

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a plane figure with twelve sides.

An architect would use this polygon when designing certain things

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The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal.

A math teacher or Mathematician would use this when creating algebra problems

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In general, this term refers to the distributive property of multiplication which states that the. Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

A mathematician would use this property when giving a new solution to a math teacher to teach to his/ her students

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The distance d between the points (x₁, y₁) and. (x ₂, y₂) is given by, Example Problem.

A police officer's speed gun uses the distance formula to see how fast people are going in their cars

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Disjunction introduction or addition (also called or introduction) is a simple valid argument form, an immediate inference and a rule of inference of propositional logic. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if P is true, then P or Q must be true.

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In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or elimination), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

A math student would use this when working on certain problems like when getting rid of non-important factors

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a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

A student would use this when working on finding the area of a circle

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a plane figure with ten straight sides and angles.

An architect would use this polygon when designing certain things like a platform

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Corresponding Angles Postulate. If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent. Converse also true: If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel.

An art teacher would use this without knowing when they are making low poly art

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the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
A math student would use this when working on certain problems like finding and comparing angles

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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. Parallel lines cut. by a transversal.

A math student would use this when working on certain problems like ones with parallel lines

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Conjunction introduction (often abbreviated simply as conjunction and also called and introduction) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof.
A math student would use this when working on certain problems

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A conclusion is a statement arrived at by applying a set of logical rules known as syllogisms to a set of premises. The process of drawing conclusions from premises and syllogisms is called deduction.

An english professor would conclude when they wanted to get their story done

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In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis.

A toy maker would use this when designing a dart board

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either of two angles whose sum is 90°.

A designer would use these angles when they are making a 90 degree angle out of 2 or more other angles

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Commutative Property of Addition and Multiplication

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Commutative Property of Addition and Multiplication

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The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.

A math student would use this when explaining their answers to multiplication problems

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The boundary line of a circle. The boundary line of a figure, area, or object. The length of such a boundary. The circumference of a circle is computed by multiplying the diameter by pi.

A math student would use this when finding the outside length of any figure

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A circle is an important shape in the field of geometry. Let's look at the definition of a circle and its parts. We will also examine the relationship between the circle and the plane. A circle is a shape with all points the same distance from its center.

An architect would use this shape when designing certain things

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A line segment connecting two points on a curve. Example: the line segment connecting two points on a circle's circumference is a chord. When the chord passes through the center of a circle it is called the diameter.A math teacher or Mathematician would use each of those in their professional work

A designer would use this when taking off parts of a circle or other objects/ shapes with curves

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A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B thereby subtending an arc between those two points whose angle is (by definition) equal to that of the central angle itself.
A person that would want to put a fountain into a park would use this by finding where it would be in the exact center and working from there.

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divide into two parts.

A chef may bisect his/ her items before they prepare food to be eaten

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Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a bi-conditional.
It would be used by someone that wants to eliminate a factor and find the right answer

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A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow . The  biconditional pq represents "p if and only  if q," where p is a hypothesis and q is a conclusion. A student may use this when trying to explain why their answer is right

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Associative Property of Addition and Multiplication

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Associative Property of Addition and Multiplication

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Parentheses show the association and the operations in the parentheses are performed first. Notice that the order of the numbers does not change – only the grouping. The associative property becomes important because it allows the mathematician, you, to add or multiply numbers with ease.
A math teacher would teach this to students when learning multiplication/ division because it is easy for them to explain and easy for students to understand

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Now 2πr is the circumference of each circle. And each circumference is an "arc" that subtends four right angles at the center. Therefore, the same ratio of arc length to radius determines a unique central angle that the arcs subtend.
Anyone that works in the car industry/ makes wheels would use this to make sure that their wheels are as round as possible