Chapter 1 Flashcards
Natural number
counting number
whole number
natural number + 0
integers
whole numbers + negative number
rational number
p/q, where p and q are integers
irrational numbers
numbers that cannot be expressed as p/q
real numbers
all irrational and rational numbers
half-open (or half-closed) intervals
only include 1 endpoint
closed intervals
include both endpoints
open intervals
do not include either endpoints
bounded intervals
finite intervals
unbounded intervals
intervals that are not bound
Interval notation
a way to describe intervals
interval notation for unbound intervals
- (infinity sign) or (infinity sign)
interval notation for closed intervals
[
interval notation for open intervals
(
Fancy e
element of
Properties of _ numbers
real
closure property
when you add or multiply two real numbers, you get a real number
exponentiation is shown by
an exponent
number that is raised by an exponent in exponentiation
base
positive integer exponent
x^2 = x *x
zero exponent on any real number =
1
Unit fraction exponent
x^1/2 = square root of x
negative number exponent
1/x^-n = x^n
rational number
x^p/q (rational number) = q root of x^p
-3^2 =
- (3*3)
(-3)^2 =
-3 * -3
x^3*x^3 =
x^6
a^5/a^2 =
a^3
A rotation that is counterclockwise has a degree of _
positive
5 ways to prove triangle congruency
SSS, SAS, ASA, AAS, HL
Ways that don’t prove triangle congruency
AA, SS, ASS
Transversal
Line that cuts parallel lines
What side lengths can be a triangle
2 lengths must be bigger than longest side length
Shortest side is always opposite of the _ angle
smallest
How to reflect over y = -x
(-y,-x)
Diagonals are perpendicular in a
kite
A kite is
2 pairs of consecutive congruent sides
A kite has _ parallel sides
no
A kite has _ pair of opposite congruent angles
1
_ sides are congruent in a parallelogram
opposite
_ sides are parallel in a parallelogram
opposite
_ angles are congruent in a parallelogram
opposite
_ angles are supplementary in a parallelogram
consecutive
Do diagonals bisect each other in a parallelogram?
yes
What is a trapezoid
1 pair of parallel sides
Base angles are _ in a isosceles trapezoid
congruent
_ are congruent in a isoscles trapezoid
diagonals
_ are congruent in Rectangle
diagonals
A rectangle is a parallelogram that has _
4 right angles
A rhombus is a parallelogram that has _
4 congruent sides
_ are perpendicular and bisect opposite angles in a rhombus
diagonals
A square is a
rectangle and rhombus
Complementary angles =
90
Supplementary angles
180
Adjacent angles
Angles that share a ray
Linear pair
angles together that make a straight line
vertical angle
angles formed by same line pair
Triangle sum theorm
All angles of triangle = 180
Exterior angle theorm
Two interior angles = exterior angle next to third interior angle of triangle
Midsegment of triangle
Middle of two adjacent sides connected
Midsegment is _ of parallel side
1/2
Median of triangle
Segment whose endpoints are a vertex and midpoint of opposite side
Centroid of triangle
All medians of triangle connect (concurrency)
Medians are divided into
thirds
Altitude of triangle
Vertex of triangle to perpendicular
Orthocenter of triangle
Point of concurrency of altitudes
Pre image and image in dilations are
similar
corresponding angles of dilations are
proportional
corresponding sides of dilations are
proportional
3 properties of similiarity
AA, SSS, SAS
180 rotation
(-x,-y)
Clockwise 90
(y, -x)
Counterclockwise
(-y,x)
Total interior angle sum
(sides-2)180
magnitude of rotational symmetry
how many degrees of rotation
In exponential relationships, the y values have
proportional differences
In linear relationships, the y values have
equal differences
point-slope equation
y-y1 = m(x-x1)
recursive function
a function that calls back on itself
0.6^2 function is downward or upward
downward
f(1)=−1.8
f(n)=f(n−1)⋅9
f(n)=−1.8⋅9 ^n−1
geometric sequence/progression
multiply previous element by constant
Arithmetic progression
difference is constant
