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Terms in this set (121)
Formed by 2 intersecting lines or segments. Always congruent.
Two angles that form a line and add up to 180°.
An angle that measures 90°.
Two angles that add up to 90°.
Alternate Interior Angles (Parallel Lines)
Ex. 3 & 6 are congruent
Alternate Exterior Angles (Parallel Lines)
Ex. 1 & 8 are congruent
Corresponding Angles (Parallel Lines)
Ex. 1 & 5 are congruent
Same Side Interior Angles (Parallel Lines)
Ex. 3 & 5 add up to 180º
Area of a Triangle
Triangle Inequality Theorem
The sum of the 2 shortest sides of a triangle is always greater than the length of the third side.
A triangle in which all three sides are equal and all three interior angles are 60°.
A triangle with two equal sides. Base angles (angles across from the congruent sides) are also equal.
Proportionality in Triangles
In every triangle, the longest side is opposite the largest angle and the smallest side is opposite the smallest angle.
Used to find the missing side of a right triangle.
"c" is always the length of the hypotenuse.
Triangles that have the same angle measures but different side lengths. Solve by setting up a proportion.
45-45-90 Special Triangle
Always in the ratio 1:1:√2
Isosceles right triangle
30-60-90 Special Triangle
Always in the ratio 1:√3:2
Three integers that, as side lengths of a triangle, form a right triangle.
Ex. 3/4/5 or 5/12/13
Degree Measure of a Triangle
The inside angles of a triangle always add up to 180°.
Area of a Circle
Degree Measure of a Circle
The central angles of a circle add up to 360°.
Circumference of a Circle
C=2πr or C=πd
Area of a Sector (Circle)
(n/360)(πr²), where n is the central angle.
Arc Length of a Sector (Circle)
(n/360)(2πr), where n is the central angle.
Area of a Polygon
A=½aP, where a is the apothem and P is the perimeter.
Sum of Interior Angles of a Polygon
Sum=180(n-2), where n is the number of sides.
Interior Angle of a Polygon
Where n is the number of sides
Degree Measure of a Quadrilateral
The interior angles of a quadrilateral add up to 360º.
Area of a Square
Diagonal of a Square
Area of a Rectangle
Perimeter of a Rectangle
Area of a Parallelogram
A=(base)(height) or A=bh
Angles in a Parallelogram
Opposite angles are equal.
Area of a Trapezoid
Surface Area of a Sphere
Surface Area of a Cylinder
Surface Area of a Prism
SA=2B+Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the prism.
Volume of a Sphere
Volume of a Cube
Volume of a Cylinder
Diagonal of a Cube
Diagonal = side√3
Volume of a Prism
(think Pythagorean theorem)
Used to find the midpoint of a line
Rate of change of a line;
rise over run;
change in y /change in x
Form 90 degree angles;
Slopes are negative reciprocals
slope = 0;
Defined by x=a, where a is a constant
slope = undefined;
Defined by y=a, where a is a constant
Use if you know the slope and the y-intercept
Use if you know the slope and a point on the line
A, B, and C are all collinear points
Average (Arithmetic Mean)
Value(s) that occurs most frequently!
Middle point of an ordered list!
Fundamental Counting Principle
If an event can happen m ways and another, independent event can happen n ways, then both events can happen in m ∗ n ways.
Probability of two independent events happening
The distance from 0 (an absolute value takes any number and makes it positive)!
Multiplying Variables with Exponents
Dividing variables with exponents
Two Exponents, one base
Base raised to the power of 0
Difference of Squares
Perfect Square Trinomials
Function Transformations: Amplitude increase of f(x) in which all values of y are multiplied by 3. A vertical stretch.
Function Transformations: Amplitude decrease of f(x) in which all values of y are multiplied by 0.5. A horizontal Stretch.
Horizontal Shift Right (ie: 3 units right)
y = f(x-3)
Horizontal Shift Left (ie: 3 units left)
y = f(x+3)
Vertical Shift up (ie: shift 2 units up)
y = f(x) + 2
Vertical Shift Down (ie: shift 2 units down)
y = f(x) - 2
Rewriting logarithms as exponentials
Logarithm Power Rule
Logarithm Product Property
Logarithm Quotient Property
Complex number i
Powers of i
Graph of y = sin(x)
Graph of y = cos(x)
Graph of y = tan(x)
Graphing Trigonometric Functions
y = Asin(Bx - C) + D
Any number that is not a decimal or a fraction. ie: -30, 1, 2, 50
Any number that is not a negative or a fraction. ie: 0, 2, 37, 455
Any integer that cannot be divided by 2 without a remainder.
ie: −111, −57, −1, 1, 67!
Any integer that can be divided by 2 without a remainder (including zero!)
ie: 2, 20, -30
Numbers that directly follow each other on a number line.
ie: −4,−3,−2,−1... or 3,4,5,6...
variable form: n, n+1, n+2, n+3
Consecutive Odd Integers
Odd numbers that follow each other on a number line.
variable form: n, n+2, n+4
Consecutive Even Integers
Even numbers that follow each other on a number line.
variable form: n, n+2, n+4, n+6
Any number that can be found on a number line. Excludes infinity and imaginary numbers.
ie: All integers, rational numbers, and irrational numbers!
Any number that can be written as a fraction (ratio of integers).
ie: 0 ,4,12 ,−5,.20!
Any number that cannot be written as a fraction.!
A positive number that can only be divided by 1 AND itself.
ie: 2, 3, 5, 7, 11, 13, 17, 19, 23, 279, 31, 37...!
(1 is NOT a prime number. 2 is the smallest prime number, and prime numbers cannot be negative or even)
The amount left over when a quantity is divided by another number.
The numbers that divide evenly into a given number without a remainder.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The numbers that divide evenly by a given number without a remainder.
Multiples of 30 are 30, 60, 90, 120
Order of Operations
Means "divided by 100"
Sum of an arithmetic sequence
Sum of a finite geometric sequence
Sum of an infinite geometric sequence where r > 1
Translating word problems: Mathematical equivalent of the word "of"
Translating word problems: Mathematical equivalent of the word "per"
Translating word problems: Mathematical equivalent of the word "percent"
Divided by 100
Translating word problems: Mathematical equivalent of the word "is"
Translating word problems: Mathematical equivalent of the word "a number"
V ariable (typically x or y)
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