A–F

AA similarity theorem
Unit 4 Lesson 3

Two triangles are similar if they have two corresponding angles that are congruent.

two triangles representing AA similarity theorem
angles and triangles with adjacent angles marked222111BACDABC
adjacent angles
Unit 3 Lesson 6

Two non-overlapping angles with a common vertex and one common side.

and are adjacent angles:

adjacent anglescommonvertexcommon side12
alternate exterior angles
Unit 3 Lesson 6

A pair of angles formed by a transversal intersecting two lines. The angles lie outside of the two lines and are on opposite sides of the transversal.

See angles made by a transversal.

lines crossing creating alternate exterior angles
alternate interior angles
Unit 3 Lesson 6

A pair of angles formed by a transversal intersecting two lines. The angles lie between the two lines and are on opposite sides of the transversal.

See also angles made by a transversal.

lines crossing creating alternate interior angles12transversalbetweenthe lines

Altitude of a triangle:

A perpendicular segment from a vertex to the line containing the base.

Altitude of a solid:

A perpendicular segment from a vertex to the plane containing the base.

altitude of triangles and cones marked ACDBHMGFEFDEJ

Two rays that share a common endpoint called the vertex of the angle.

lines creating angles
angle bisector
Unit 3 Lesson 4

A ray that has its endpoint at the vertex of the angle and divides the angle into two congruent angles.

a line cutting and angle in half
angle of depression/angle of elevation
Unit 4 Lesson 9

Angle of depression: the angle formed by a horizontal line and the line of sight of a viewer looking down. Sometimes called the angle of decline.

Angle of elevation: the angle formed by a horizontal line and the line of sight of a viewer looking up. Sometimes called the angle of incline.

angle of elevation ad depression horizontalhorizontalangle ofdepressionangle ofelevation
angle of rotation
Unit 1 Lesson 3

The fixed point a figure is rotated about is called the center of rotation. If one connects a point in the pre-image, the center of rotation, and the corresponding point in the image, they can see the angle of rotation. A counterclockwise rotation is a rotation in a positive direction. Clockwise is a negative rotation.

angle of rotationpositive rotationD is the center of rotationnegative rotation
angles made by a transversal
Unit 3 Lesson 6
angles made by transversalcorresponding anglessame-side interior anglesAngles made by atransversal andparallel linesalternate exterior anglesalternate interior angles12135416

A line that a graph approaches, but does not reach. A graph will never touch a vertical asymptote, but it might cross a horizontal or an oblique (also called slant) asymptote.

Horizontal and oblique asymptotes indicate the general behavior of the ends of a graph in both positive and negative directions. If a rational function has a horizontal asymptote, it will not have an oblique asymptote.

Oblique asymptotes only occur when the numerator of has a degree that is one higher than the degree of the denominator.

a diagram showing vertical asymptotes between curvesverticalasymptoteverticalasymptote
a diagram showing the oblique asymptote within a 1/x functionobliqueasymptote
a diagram showing the horizontal asymptote within a 1/x functionhorizontal asymptote
auxiliary line
Unit 2 Lesson 5

An extra line or line segment drawn in a figure to help with a proof.

auxiliary line12345

is an auxiliary line (added to the diagram of to help prove that the sum of the angles .

A polynomial with two terms.

a binomial of (ax b)termtermaddition or subtraction
bisect (verb); bisector (noun) (midpoint)
Unit 1 Lesson 5

To divide into two congruent parts.

A bisector can be a point or a line segment.

bisector

A perpendicular bisector divides a line segment into two congruent parts and is perpendicular to the segment.

bisector
center of dilation
Unit 4 Lesson 1

See dilation.

All points in a plane that are equidistant from a fixed point called the center of the circle. The circle is named after its center point. The distance from the center to the circle is the radius. A line segment from the center point to a point on the circle is also called a radius (plural radii, when referring to more than one).

Notation:

circleradiusradius
circumscribe
Unit 2 Lesson 2

To draw a circle that passes through all of the vertices of a polygon. The circle is called the circumcircle.

All of these polygons are inscribed in the circles.

circumscribe
clockwise / counterclockwise
Unit 1 Lesson 1

clockwise: Moving in the same direction, as the hands on a clock move.

counterclockwise: Moving in the opposite direction, as the hands on a clock move.

a clock with labels for counterclockwise and clockwise directions

A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set.

A diagram showing that 5 2=7 is closed under addition and 2-5=-3 is not closed under subtraction5 and 2 and 7 are natural numbersThe natural numbers areclosed under addition2 and 5 are natural numbersThe natural numbers are NOTclosed under subtraction-3 isNOT anaturalnumber.
coincides (superimposed or carried onto)
Unit 1 Lesson 2, Unit 2 Lesson 4

When working with transformations, we use words like coincide, superimposed, or carried onto to refer to two points or line segments that occupy the same position on the plane.

collinear, collinearity
Unit 4 Lesson 1

When three or more points lie in a line.

Note: Any two points can define a line.

Noncollinear: Not collinear.

collinearPoint S isnoncollinearwith V and T.

complement (in probability)
Unit 8 Lesson 4

The complement of an event is the subset of outcomes in the sample space that are not in the event. This means that in any given experiment, either the event or its complement will happen, but not both. The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

complementary angles
Unit 4 Lesson 8

Two angles whose measures add up to .

complementary angles
completing the square
Unit 5 Lesson 6

Completing the Square changes the form of a quadratic function from standard form to vertex form. It can be used for solving a quadratic equation and is one method for deriving the quadratic formula.

complex conjugates
Unit 6 Lesson 8

A pair of complex numbers whose product is a nonzero real number.

The complex numbers and form a conjugate pair.

The product , a real number.

The conjugate of a complex number is the complex number .

The conjugate of a complex number is represented with the notation .

complex number
Unit 6 Lesson 8

A number with a real part and an imaginary part. A complex number can be written in the form , where and are real numbers and is the imaginary unit.

When , the complex number can be written simply as It is then referred to as a pure imaginary number.

the complex number defined as a bi with the square root of negative 1=ithe “a” and “b” are real.imaginary
concave and convex
Unit 4 Lesson 5

Polygons are either convex or concave.

Convex polygon— no internal angle that measures more than . If any two points are connected with a line segment in the convex polygon, the segment will lie on or inside the polygon.

Concave polygon—at least one internal angle measures more than . If it’s possible to find two points on the polygon that when connected by a line segment, the segment exits the concave polygon.

concave and convexAAABBBCCCDDDEEEWWWXXXYYYZZZVVVinside or on edgeoutside the polygonconvexconcave
concentric circles
Unit 1 Lesson 3

Circles with a common center.

concentric circles
conditional frequency
Unit 8 Lesson 1

See two-way relative frequency table.

conditional probability
Unit 8 Lesson 2

The measure of an event, given that another event has occurred.

The conditional probability of an event is the probability that the event will occur, given the knowledge that an event has already occurred. This probability is written , notation for the probability of given .

The likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.

Notation: The probability that event will occur given the knowledge that event has already occurred.

In the case where and are independent (where event has no effect on the probability of event ); the conditional probability of event given event is simply the probability of event , that is,

If events and are not independent, then the probability of the intersection of and (the probability that both events occur) is defined by

From this definition, the conditional probability is obtained by dividing by :

conditional statement
Unit 3 Lesson 4

A conditional statement (also called an “if-then” statement) is a statement with a hypothesis , followed by a conclusion . Another way to define a conditional statement is to say, “If this happens, then that will happen.” .

The converse of a conditional statement switches the conclusion , and the hypothesis to say: .

A true conditional statement does not guarantee that the converse is true.

Examples: conditional statement: If it rains, the roads will be wet.

Converse: If the roads are wet, then it must have rained.

The converse is not necessarily true. Perhaps a pipe broke and flooded the road.

congruence statement
Unit 2 Lesson 1

A mathematical statement that uses the symbol. Examples:

Only figures or shapes can be congruent. Numbers are equal.

Two triangles (figures) are congruent if they are the same size and same shape. Two geometric figures are defined to be congruent if there is a sequence of rigid motions that carries one onto the other.

The symbol for congruent is .

If it’s given that two triangles (figures) are congruent, then the Corresponding Parts of the Congruent Triangles (figures) are Congruent (CPCTC).

conjecture
Unit 1 Lesson 6

A mathematical statement that has not yet been rigorously proven. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases. When a conjecture is proven, it becomes a theorem.

constant of proportionality/ constant of variation
Unit 7 Lesson 2

The constant of proportionality (also called constant of variation) is encountered in direct variation and inverse variation equations.

It is usually symbolized by .

construction
Unit 2 Lesson 1

Creating a diagram of geometric figures and items such as perpendicular lines or a regular pentagon using only a compass and straightedge.

A construction yields an exactly reproducible and unambiguous result, of which all properties can be measured as expected (within the accuracy of the instruments use.)

Constructing an angle bisector:

construction
converse statement
Unit 3 Lesson 4, Unit 3 Lesson 7

See conditional statement.

corresponding angles
Unit 2 Lesson 3, Unit 3 Lesson 6

Angles that are in the same relative position.

corresponding angles1212
corresponding parts (in a triangle)
Unit 2 Lesson 4

The word corresponding refers to parts that match between two congruent figures. Corresponding angles and corresponding sides will have the same measurements in congruent figures.

corresponding parts (in a triangle)
corresponding points / sides
Unit 1 Lesson 2, Unit 2 Lesson 3

Points, sides, and angles can all be corresponding. It means they are in the same relative position.

counterexample
Unit 2 Lesson 4

An example that disproves a statement or conjecture. One counterexample can disprove a conjecture based on many examples.

Statement: All blondes drive red cars.

Counterexample: My mom is blonde, but her car is silver.

See congruent (CPCTC).

A value that, when multiplied by itself, three times gives the number.

Example:

, so the cube root of is or .

, so the cube root of is or .

The mathematical symbol that indicates to find the cube root is a radical sign with a small on the outside. .

definition
Unit 3 Lesson 5

A statement of the meaning of a word or symbol that is accepted by the mathematical community. A good mathematical definition uses previously defined terms and the symbol that represents it. Once a word has been defined, it can be used in subsequent definitions.

A degree is the measure of an angle of rotation that is equal to of a complete rotation around a fixed point. A measure of degrees would be written as .

Any line segment that connects nonconsecutive vertices of a polygon.

diagonalnonconsecutiveverticesADCGHIEFB

A transformation that produces an image that is the same shape as the pre-image but is of a different size. A description of a dilation includes the scale factor and the center of dilation.

A dilation is a transformation of the plane, such that if is the center of the dilation and a nonzero number is the scale factor, then is the image of point , if , , and are collinear and .

dilation
direct variation
Unit 7 Lesson 2
UntitledDirect Variation

See mutually exclusive.

equality statements
Unit 2 Lesson 1

A mathematical sentence that states two values are equal.

It contains an equal sign.

equidistant
Unit 3 Lesson 5

A shortened way of saying equally distant; the same distance from each other or in relation to other things.

equilateral, equilateral triangle
Unit 1 Lesson 4

Equilateral means equal side lengths.

In an equilateral triangle, all of the sides have the same length.

equilateral, equilateral triangle
exterior angle of a triangle (remote interior angles)
Unit 3 Lesson 6

An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side of the triangle. There are two exterior angles at every vertex of a triangle.

exterior angle of a triangle (remote interior angles)extended sideexterior angleremoteinteriorangles
exterior angle theorem
Unit 3 Lesson 6

The measure of an exterior angle in any triangle is equal to the sum of the two remote interior angles.

exterior angle theorem83°62°145°
extraneous solution
Unit 7 Lesson 3

A derived solution to an equation that is invalid in the original equation.

factored form of a quadratic function
Unit 5 Lesson 3

Go to quadratic function.

false negative/positive
Unit 8 Lesson 2

The result of a test that appears negative when it should not. An example of a false negative would be if a particular test designed to detect cancer returns a negative result, but the person actually does have cancer.

A false positive is where you receive a positive result for a test, when you should have received a negative result.

flow proof
Unit 3 Lesson 4

See proof: types—flow, two-column, paragraph.

Fundamental Theorem of Algebra
Unit 6 Lesson 7

An degree polynomial function has roots, but some of those roots might be complex numbers.

diagrams showing the the the degree of a polynomial and the roots of that polynomial are the same

G–L

geometric mean
Unit 4 Lesson 6

A special type of average where numbers are multiplied together and then the root is taken. For two numbers, the geometric mean would be the square root. For three numbers, it would be the cube root.

Example: The geometric mean of and is .

The geometric mean of two numbers and is the number such that .

A six-sided polygon.

hexagon
horizontal asymptote
Unit 7 Lesson 7

A line that the graph approaches but does not reach. Exponential functions have a horizontal asymptote. The horizontal asymptote is the value the function approaches as either gets infinitely larger or smaller. An asymptote is an imaginary line, but it is often shown as a dotted line on the graph.

As gets smaller, the graph of approaches the horizontal asymptote, .

the graphs of f(x)=2^x and its horizontal asymptote of y=0x–10–10–10–5–5–5555y–5–5–5555101010000

As gets larger, the graph of approaches the horizontal asymptote, .

the graphs of f(x)=2^-x and its horizontal asymptote of y=0x–5–5–5555101010y–5–5–5555101010000

As gets smaller, the graph of approaches the horizontal asymptote, .

the graphs of f(x)=2^x-3 and its horizontal asymptote of y=-3x–10–10–10–5–5–5555y–5–5–5555101010000

See also asymptote.

horizontal shift
Unit 5 Lesson 4

See transformations on a function.

hypotenuse
Unit 4 Lesson 7

The longest side in a right triangle.

The side opposite the right angle.

hypotenuseACB

A picture; a visual representation of a thing. See pre-image / image.

imaginary number
Unit 6 Lesson 8

See complex number.

independent event / dependent event
Unit 8 Lesson 5

When two events are said to be independent of each other, the probability that one event occurs in no way affects the probability of the other event occurring.

When you flip two coins, each flip is an independent event.

independent event independent eventsevent 1event 2coinHTTHcoin

An event is dependent if the occurrence of the first event affects the occurrence of the second so that the probability is changed.

Example: Suppose there are balls in a box. What is the chance of getting a green ball out of the box on the first try? A green ball is selected and removed in event . What is the chance of getting a green ball on the second try?

dependent eventindependentdependent
inscribed in a circle
Unit 2 Lesson 2
inscribed in a circle
intersection of sets
Unit 8 Lesson 4

The intersection of two sets and , is the set containing all of the elements of that also belong to . The symbol for intersection is .

For example: If and then .

inverse trigonometric ratio
Unit 4 Lesson 9

The inverse of a trigonometric function is used to obtain the measure of an angle when the trigonometric ratio is known.

Example: The inverse of sine is denoted as arcsine, or on a calculator it will appear as .

If and the measure of the angle is needed, write to express this. The answer to the expression is the measure of the angle.

inverse trigonometric ratio

All of the inverse trigonometric functions are written the same way.

inverse variation
Unit 7 Lesson 5
UntitledInverse Variation

Events that can occur at the same time.

Two-way tables show joints. See two-way tables.

The vertical line that divides the graph into two congruent halves, sometimes called axis of symmetry.

The equation for the line of symmetry in a coordinate plane is always:

line of symmetryx–6–6–6–4–4–4–2–2–2y–2–2–2222444000
linear function
Unit 5 Lesson 1
several diagrams modeling linear functions, including tables and graphs. Equations for linear functions are defined as y=mx b, y=m(x-x1) y1, and Ax By=Clinear functionslope-intercept formm = slopeb = y-interceptpoint-slope formyou need slope and a point:standard formdomain: all real numbersrange: all real numbersunless restricted. unless restricted.graph is a linerate of change (slope) is constant1st difference is constantThe function can increase,decrease, or remain constant. 2122
linear pair
Unit 3 Lesson 6

Two supplementary angles that share a vertex and a side.

A linear pair always make a line.

linear pair125°55°vertexcommon side

M–R

marginal frequency
Unit 8 Lesson 1

See two-way tables.

median in a triangle
Unit 3 Lesson 4

A line segment in a triangle that extends from any vertex to the midpoint of the opposite side.

median in a triangle
midline of a triangle
Unit 4 Lesson 2

is the midline of .

midline of a trianglemidline
midline of a triangle theorem
Unit 4 Lesson 2

The midline of a triangle or the midsegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

A point on a line segment that divides it into two equal parts.

The formula for finding half the distance between two points (or the midpoint ) in a coordinate grid is:

midpointx–4–4–4–3–3–3–2–2–2–1–1–1111222333444y–3–3–3–2–2–2–1–1–1111222333444000(-3, -2)(-3, -2)(-3, -2)(-0.5, 1)(-0.5, 1)(-0.5, 1)(2, 4)(2, 4)(2, 4)midpoint

See also bisect.

model, mathematical
Unit 4 Lesson 10

Modeling with mathematics is the practice of making sense of the world through a mathematical perspective. A mathematical model could be an equation, graph, diagram, formula, sketch, computer program, or other representation that will help you to study different components of a function or to make predictions about behavior.

mutually exclusive
Unit 8 Lesson 5

Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0.

mutually exclusive event
Unit 8 Lesson 5

Both events can’t happen at the same time. It must be one or the other, but not both.

Example: heads and tails are mutually exclusive when flipping a coin.

A polygon with number of sides.

See polygon.

number sets (systems)
Unit 6 Lesson 1

Your first experience with number sets was probably when you learned to count. This set is called the Natural numbers, . When you added the set grew to be the Whole numbers, . The need for Integers, , arose when you subtracted a large number from a smaller number. Then you needed the Rational numbers, , when you started dividing. Other number sets (or systems) are needed in more advanced mathematics.

number setsRealRationalIntegerWholeNaturalIrrationalImaginaryComplexThe Number System

An eight-sided polygon.

octagon
opposite angles, opposite vertices
Unit 1 Lesson 4, Unit 1 Lesson 5

Opposite angles in a quadrilateral do not share a side.

A vertex (plural, vertices) is part of an angle.

opposite angles, opposite verticesvertexvertex
opposite side in a triangle
Unit 4 Lesson 7

A side opposite an angle in a triangle is the side that is not part of the angle.

opposite side in a triangleAMNLBCside oppositeangle Aside oppositeangle L
opposite sides (in a parallelogram or an even-sided polygon)
Unit 1 Lesson 4, Unit 1 Lesson 5

If two sides in a parallelogram are parallel, they must be opposite sides.

If two sides in an even-sided polygon are parallel, they must be opposite sides.

opposite sides (in a parallelogram or an even-sided polygon)ABCDRMNOPQ

The orientation is determined by the order in which a figure’s vertices are labeled. In the diagram, the vertices of the green pentagon are labeled from to to to to in a clockwise direction.

In the blue pentagon, the orientation of the vertices has changed. The corresponding vertices go in a counterclockwise direction from to to to to .

orientationLMNJKL'K'J'M'N'

The origin is a starting point. The coordinates for every other point are based on how far that point is from the origin. At the origin, both and are equal to zero, and the -axis and the -axis intersect.

The graph of every equation that can be written in the form , where is in the shape of a parabola. It looks a bit like a U but it has a very specific shape. Moving from the vertex, it is the exact same shape on the left as it is on the right. (It is symmetric.)

The graph of the parent function or

follows the pattern:

  • move right 1 step, move up or

  • move right 2 steps, move up or

  • move right 3 steps, move up or

parabolax–3–3–3–2–2–2–1–1–1111222333y111222333444555666777888999000vertex
parallelogram
Unit 1 Lesson 4

A quadrilateral in which the opposite sides are parallel.

parallelogram

A five-sided polygon.

pentagon

The line (line segment or ray) that divides a line segment into two equal lengths and makes a right angle with the line segment it divides.

perpendicular bisector

Any 2-D shape formed with line segments that connect at their endpoints, making a closed figure. The location where any two line segments connect is called a vertex.

polygonpolygonnot a polygon

Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name identifies how many sides the shape has. For example, a triangle has three sides, a quadrilateral has four sides, a pentagon five sides, and an octagon eight sides. A regular polygon is made up of congruent line segments.

In a regular polygon, all sides are congruent, and all angles are congruent.

A simple and useful statement in geometry that is accepted by the mathematical community as true without proof.

pre-image / image
Unit 1 Lesson 1

The pre-image is the original figure. The image is the new figure created from the pre-image through a sequence of transformations or a dilation.

pre-image / image
preserves distance and angle measure
Unit 1 Lesson 3

Measurements are not changed under a rigid transformation.

proof by contradiction
Unit 2 Lesson 4

A way to justify a claim is to use a proof by contradiction method, in which one assumes the opposite of the claim is true, and shows that this leads to a contradiction of something that is known to be true.

proof: types—flow, two-column, paragraph
Unit 3 Lesson 3
proof: types—flow, two-column, paragraph
properties of equality
Unit 3 Lesson 3

The properties of equality describe operations that can be performed on each side of the equal sign ( ) and still ensure that the expressions remain equivalent.

In the table below, , , and stand for arbitrary numbers in the rational, real, or complex number systems. The properties of equality are true in these number systems.

Reflexive property of equality

Symmetric property of equality

If , then

Transitive property of equality

If and , then

Addition property of equality

If , then

Subtraction property of equality

If , then

Multiplication property of equality

If , then

Division property of equality

If and , then

Substitution property of equality

If , then may be substituted for in any expression containing

proportion: proportionality statement
Unit 4 Lesson 4

A proportion is a statement that two ratios are equal.

proportion: proportionality statement
quadratic formula
Unit 6 Lesson 5

The quadratic formula allows us to solve any quadratic equation that’s in the form . The letters , , and in the formula represent the coefficients of the terms.

quadratic formula
quadratic function
Unit 5 Lesson 1
Several diagrams representing a quadratic function, including an area model, growing steps, a 2nd difference table, and parabolic graphs.quadratic functionvertex formfactored formstandard formgraph is a parabola
quadratic inequality
Unit 6 Lesson 10

A function whose degree is and where the is not always exactly equal to the function. These types of functions use symbols called inequality symbols that include the symbols we know as less than , greater than , less than or equal to , and greater than or equal to .

Example:

A quadrilateral is a four-sided polygon. See the diagram for various types of quadrilaterals.

quadrilaterals: types rhombussquarerectangleparallelogramquadrilateral

A radical is the mathematical inverse of an exponent. This is the symbol for a radical: . It is also called a square root symbol, but that is only when it’s asking for the number that when multiplied by itself gives you the number inside the . (The is not usually written.) It can be used to indicate a cube root , a fourth root , or higher. (A root that is higher than is written in.)

Plural of radius. See circle.

A ratio compares the size or amount of two values.

Here is a sentence that compares apples to oranges as shown in the diagram below: “We have five apples for every three oranges.” It describes a ratio of to or . A ratio can also be written as a fraction, in this case .

Compare oranges to apples. The ratio changes to or .

The two previous ratios are called part-to-part ratios. Another way to write a ratio is to compare a part to a whole.

Compare apples to the total amount of fruit. The ratio changes to or .

ratio

Ratios can be scaled up or down. There are bags of fruit, each containing oranges and apples. The ratio to still represents the number of apples compared to the number of oranges. But the ratio to also compares the number of apples to the number of oranges.

rational exponent (fractional exponent)
Unit 6 Lesson 1

Rational exponents (also called fractional exponents) are expressions with exponents that are rational numbers (as opposed to integers).

A part of a line that has a fixed starting point (endpoint), and then continues toward infinity.

Notation: ray

A ray is named using its endpoint first, and then any other point on the ray.

ray
reasoning – deductive/inductive
Unit 3 Lesson 1

Two Types of Reasoning

Inductive reasoning:

from a number of observations, a general conclusion is drawn.

Deductive reasoning:

from a general premise (something we know), specific results are predicted.

Observations

General Premise

Each time I make two lines intersect, the opposite angles are congruent. I have tried this 20 times and it seems to be true.

Conclusion:

Opposite angles formed by intersecting lines are always congruent.

reasoning – deductive/inductive1234

Given: Angles 1, 2, 3, and 4 are formed by two intersecting lines.

Prove: Opposite angles formed by intersecting lines are always congruent.

reasoning – deductive/inductive

See quadrilaterals: types.

reference angle
Unit 4 Lesson 7

The acute angle between the terminal ray of an angle in standard position and the -axis.

reference angle

A reflection is a rigid transformation (isometry). In a reflection, the pre-image and image points are the same distance from the line of reflection; the segment connecting corresponding points is perpendicular to the line of reflection.

The orientation of the image is reversed.

a reflection of a polygon over a line
regular polygon
Unit 1 Lesson 4

See polygon.

relative frequency table (statistics)
Unit 8 Lesson 1

When the data in a two-way table is written as percentages

See two-way frequency table.

A quadrilateral in which all sides are congruent.

rhombus
rigid transformation
Unit 1 Lesson 1

Also called an isometry. The word rigid means that the pre-image and image are congruent. The rigid transformations include translation, rotation, and reflection.

roots: real and imaginary
Unit 6 Lesson 7

The solutions of an equation in the form .

A rotation is a rigid transformation. In a rotation, all points remain the same distance from the center of rotation, move in the same direction, and through the same central angle. The orientation of the pre-image remains the same.

rotationcenter of rotation
rotational symmetry
Unit 1 Lesson 4

See symmetry.

S–X

same-side interior angles
Unit 3 Lesson 6

See angles made by a transversal.

same-side interior anglesDBFCAG13
SAS triangle similarity
Unit 4 Lesson 3

See triangle similarity.

scale factor
Unit 4 Lesson 1

The ratio of any two corresponding lengths in two similar geometric figures.

scale factor
side-splitter theorem
Unit 4 Lesson 4

The side-splitter theorem is related to the midline of a triangle theorem. It extends the rule to say if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally.

similarity
Unit 4 Lesson 3

A 2-D figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

special right triangles
Unit 4 Lesson 11

There are two special right triangles. They are special because they can be solved without using trigonometry.

two 45°-45°-90°right triangles with their sides labeled45°45°45°45°If hypotenuse is known (x), then side is45 - 45 right triangleIf side lengths are known (x),then the hypotenuse is
three 30°-60°-90°right triangles with their sides labeled60°30°30°60°30°60°If side opposite 60° is known (x), then hypotenuse isand side opposite 30° isand the side opposite 30° isIf hypotensue is known (x),then side opposite of 60° is

See quadrilaterals: types.

square root
Unit 6 Lesson 1

The square root of a number is one of the two identical factors that when multiplied together equal the number.

Example: 6, so a square root of is .

Note that too. That means is also a square root of . The mathematical symbol that indicates to find the square root is a radical sign .

square root function
Unit 7 Lesson 1

A function that has a radical (square root sign) and the independent variable is under the square root sign .

Equation:

Domain:

Range:

Always increasing

Untitledx222444666y222444000
SSS triangle similarity
Unit 4 Lesson 3

See triangle similarity.

standard form of a quadratic function
Unit 5 Lesson 8

straight angle
Unit 3 Lesson 6

When the legs of an angle are pointing in exactly opposite directions, the two legs form a single straight line through the vertex of the angle. The measure of a straight angle is always . It looks like a straight line.

straight angle180°180°180°PNM
supplementary angles
Unit 3 Lesson 6

Two angles whose measures add up to exactly .

supplementary anglesCBADEF∠ABC and ∠DEF are supplementary

If a figure can be folded or divided in half so that the two halves match exactly, then such a figure is called a symmetric figure. The fold line is the line of symmetry.

symmetricline of symmetry

A line that reflects a figure onto itself is called a line of symmetry.

A figure that can be carried onto itself by a rotation is said to have rotational symmetry.

symmetryThe rotation of 72° will makethis figure look the same.72°72°line of symmetry
tessellation
Unit 3 Lesson 6

A tessellation is a regular pattern made up of flat shapes repeated and joined together without any gaps or overlaps. Many regular polygons tessellate, meaning they can fit together without any gaps.

tessellation

A theorem is a statement that can be demonstrated to be true by using definitions, postulates, properties, and previously proven theorems.

The process of showing a theorem to be correct is called a proof.

transformations on a function (non-rigid)
Unit 5 Lesson 4

A dilation is a nonrigid transformation because the shape changes in size. It will make the function change faster or slower depending on the value of . If , it will grow faster and look like it has been stretched. If , the function will change more slowly and will appear to be fatter. A dilation is also called a vertical stretch.

Untitledx–4–4–3–3–2–2–1–11122334455y–2–2–1–1112233445500
transformations on a function (rigid)
Unit 5 Lesson 4

A shift up, down, left, or right, or a vertical or horizontal reflection on the graph of a function is called a rigid transformation.

Vertical shift

Up when

Down when

The vertical shift of a parabolax–4–4–4–3–3–3–2–2–2–1–1–1111y–1–1–1111222333000

Horizontal shift

Left when

Right when

the horizontal shift of a parabolax–3–3–3–2–2–2–1–1–1111222333444y–2–2–2–1–1–1111222333000

Reflection

reflection over the -axis

The reflection of a parabola over the x axisx–1–1–1111y–1–1–1111000

reflection over the -axis

the reflection of a cubic function over the y axisx–1–1–1111y–1–1–1111000

A dilation is a nonrigid transformation. It will make the function changes faster or slower depending on the value of . If , it will grow faster and look like it has been stretched. If , the function will grow more slowly and will appear to be fatter.

translation
Unit 1 Lesson 1

A translation is a rigid transformation.

translationcongruenttranslationEach point moves samedistance and same direction.
transversal
Unit 3 Lesson 6

A line that passes through two lines in the same plane at two distinct points. The two lines do not need to be parallel. But when the lines are parallel, several special angle relationships are formed.

transversal

A quadrilateral with exactly one pair of parallel opposite sides.

(Note: A trapezoid can also be defined as a quadrilateral with at least one pair of opposite sides that are parallel. This definition makes it possible for parallelograms to be a special type of trapezoid.)

In an isosceles trapezoid, the two opposite sides that are not parallel are congruent and form congruent angles with the parallel sides. This feature of an isosceles trapezoid only exists if the trapezoid is not a parallelogram.

trapezoidisosceles trapezoid
tree diagram
Unit 8 Lesson 2

A tool in probability and statistics used to calculate the number of possible outcomes of an event, as well as list those possible outcomes in an organized manner.

tree diagram
triangle congruence criteria: ASA, SAS, AAS, SSS
Unit 2 Lesson 4

Two triangles are congruent if all three sides and all three angles are congruent. But sometimes only three pieces of information are sufficient to prove two triangles congruent.

ASA stands for “angle-side-angle.”

triangle congruence criteria: ASA

SAS stands for “side-angle-side.”

triangle congruence criteria: sas

AAS stands for “angle-angle-side.”

triangle congruence criteria:aas

SSS stands for “side-side-side.”

triangle congruence criteria: sss
triangle similarity
Unit 4 Lesson 3

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. Similar triangles are the same shape, but not necessarily the same size.

There are three similarity patterns that provide sufficient information to prove two triangles are similar:

AA Similarity

SAS Similarity

SSS Similarity

trigonometric ratios in right triangles: sine A, cosine A, tangent A
Unit 4 Lesson 7

An operation that relates the measure of an angle with a ratio of the lengths of the sides in a right triangle. There are three trigonometric ratios, plus their reciprocals. See Reciprocal trigonometric functions for definitions.

abbreviated

abbreviated

abbreviated

A trigonometric ratio always includes a reference angle.

In right triangle , the trigonometric ratios are defined as:

trigonometric ratios in right triangles: sine A, cosine A, tangent A

Note that each trigonometric function above references the angle . If angle was referenced as the angle, the opposite and adjacent sides would be in reference to angle , and they would switch sides.

A polynomial with three terms.

a diagram showing ax^2 bx c has 3 terms3 terms
two-column proof
Unit 3 Lesson 3

See proof:types—flow, two-column, paragraph.

two-way frequency and two-way relative frequency table
Unit 8 Lesson 1

A two-way frequency chart simply lists the number of each occurrence.

Average is more than 100 texts sent per day

Average is less than 100 texts sent per day

Total

# of Teenagers

20

4

24

# of Adults

2

22

24

Totals

22

26

48

In a two-way relative frequency table, each number in the cells is divided by the grand total. That is because we are looking for a percentage that shows us how the data compares to the grand total.

Average is more than 100 texts sent per day

Average is less than 100 texts sent per day

Total

% of Teenagers

42%

8%

50%

% of Adults

4%

46%

50%

% of Total

46%

54%

100%

In this table, the ‘inner’ values represent a percent and are called conditional frequencies. The conditional values in a relative frequency table can be calculated as percentages of one of the following:

  • the whole table (relative frequency of table)

  • the rows (relative frequency of rows)

  • the columns (relative frequency of column)

A table listing two categorical variables whose values have been paired such that the possible values of one variable make up the rows and the possible values for the other variable make up the columns. The green cells on this table are where the joint frequency numbers are located. They are called joint frequency because you are joining one variable from the row and one variable from the column. The marginal frequency numbers are the numbers on the edges of a table. On this table, the marginal frequency numbers are in the purple cells.

two-way tableAverage is more than100 texts a dayAverage is less than100 texts a day% of teenagers% of adults% of totaljoint frequencynumbersjoint frequencynumbersjoint frequencynumbersjoint frequencynumbersmarginal frequencynumbersmarginal frequencynumbersTotalmarginalfrequencyfrequencygrand total

The union of two sets is a set containing all elements that are in set or in set (or possibly both). The symbol for union is .

For example, .

See angle.

See quadratic function.

vertical angles
Unit 3 Lesson 6

The angles opposite each other when two lines cross. They are always congruent.

vertical angles1234
vertical asymptote
Unit 7 Lesson 7

See asymptote.

vertical shift
Unit 5 Lesson 4

See transformations on a function (rigid).

vertical stretch
Unit 5 Lesson 4

See transformations on a function (non-rigid).

x-intercept
Unit 6 Lesson 7

The point(s) where a line or a curve cross the -axis. The -value of the point will be . A non-horizontal line will only cross the -axis once. A curve could cross the -axis several times.

a line passing through the points (-5,0) and (0,2)x–6–6–6–4–4–4–2–2–2y222000(-5, 0)(-5, 0)(-5, 0)
a parabola with a vertex at (-1,-4) passing through the points (-3,0) and (1,0)x–4–4–4–2–2–2222y–4–4–4–2–2–2222000(-3, 0)(-3, 0)(-3, 0)(1, 0)(1, 0)(1, 0)

Y–Z

zeros, roots, solutions
Unit 6 Lesson 7

The real solutions to a quadratic equation are where it is equal to zero. They are also called zeros or roots. Real zeros correspond to the -intercepts of the graph of a function.

a parabola with the vertex A and passing through the points B(10,0) and C(2,0)x222444666888101010121212141414y–6–6–6–4–4–4–2–2–22224440002 and 10 are theof the quadraticzerosrootssolutionsx-intercepts