Math 8 final notes

Interior angles

3, 4, 6, 5

exterior angles

1, 2, 7, 8

Alternate interior angles

3 and 6, 4 and 5

Alternate exterior angles

2 and 7, 8 and 1

Verical angles

1 and 4, 5 and 8

adjacent angles

1 and 3, 5 and 7, 6 and 8, 2 and 4

complementary angles add up to

90 degrees

supplementary angles

1 and 2, 5 and 6, 7 and 8, 3 and 4

supplementary angles add up to

180 degrees

equation to solve:

r + r = ext

or

c + d = a

equation to solve

a + b + c = 180

what transformation is this

transformation (slide)

what transformation is this

reflection (flip)

flip over an axis

what transformation is this

Rotation (turn)

turn 90 degrees or 180 degrees, always counterclockwise unless specified as clockwise

what transformation is this

dilation (enlarge or reduce)

Transformations type: When the figure is congruent (equal) to the original firgure

Rigid

What transformations are rigid?

Reflections

Translations

Rotations

Transformations type: when the new figure is similar (not congruent) to the original figure - the size changes

non-rigid

What transformations are non-rigid?

dilations

Slope type?

Positive slope

Slope type?

Negative slope

Slope type?

zero slope (0,0)

Slope type?

undefined slope

How to find a slope?

y(2) - y(1)

————-

x(2) - y (2)

How to find a slope?

The line passing through (-2, 3) and (2, -1)

6x + 2y = 24 in slope-intercept form

y = -3x + 12

6x + 2y = 24

-6x -6x

---

2y = -6x + 24

— ———- ==

2 2

y = -3x + 12

finding slope on a graph

rise

—-

run

3 / 5

What line is this?

Horizontal

equation and slope of horizontal line

equation of the form y = c

Slope of 0

equation and slope of vertical line

equation of the form x = a

Undefined slope

What does an 180 degree change do to a plotted point

changes negative to a positive and a positive to a negative

how do you know if points make a function?

example: (4,5) (3,2) (5,5) (2,-3)

If all X's (x,y) are different, it is functional

could 8, 11, and 16 make a triangle?

yes, the two legs must make a greater sum than the largest leg

what type of triangle is this

right

what type of triangle is this

isosceles

What type of triangle is this

equilateral

what type of triangle is this

scalene

Scalene triangle definition

A scalene triangle is a triangle in which all three sides have different lengths, and all three angles have different measures

equilateral triangle definition

An equilateral triangle is a polygon with three equal sides and three equal angles. It is the most symmetrical type of triangle and serves as a fundamental shape in geometry

isosceles triangle definition

An isosceles triangle is a triangle that has at least two sides of equal length. Because its sides correspond to its angles, an isosceles triangle also has two base angles of equal measure.

right triangle definition

a triangle with exactly one interior angle of 90°

input and output rule

every input needs an output

Discrete definition

Whole numbers that can be counted

continuous

measurables

which table is nonlinear

B

what is the vertical line test?

putting vertical lines on a graph to see if any points are touched by the same vertical line. If so, it is nonlinear.

rate of change is:

the slope

zero exponents

0 = 1

negative exponent rule

put negative into a function

power to a power exponent rule

multiply the exponents

dividing with exponents rule

subtract exponents

multiplying with exponents rule

add the exponents

rational numbers definition

any number that can be written as a fraction

integers and whole numbers and natural numbers definition

irrational number definition

cannot be expressed as a fraction

…

rational numbers decimal form

termination or repeating

irrational numbers decimal form

non-terminating and non-repeating

irrational numbers are

square root of non-perfect squares

cube root of non-perfect cubes

pi

triangle inequality theorem

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.

which number is the y-intercept

-1

what is a y-intercept?

The line that goes through the y axis on a graph. The staring point of a slope.

What is the slope?

-2/3x

what is the standard form?

B

What is the standard form?

D

What does congruent mean for a shape?

The same shape and the same size

What does similar mean for a shape

The same shape, different size

(-3, 3)

Both numbers just turn the opposite, and are half because dialated by 1/2 (positive or negative)

D

Steps to solve equation

subtract 3 on both sides

divide number by -4x

Will a scientific notation with a positive exponent have a small or large standard form

large

Will a scientific notation with a negative exponent have a small or large standard form

small

To determine what scientific notation is greater, what do we look at?

The exponent on 10

(3 × 10^3) (2 x 10^5)

given this equation, what is the steps to solving into one scientific notation

add the exponents

multiply the coefficients by each other

this is not in proper scientific notation, when fixed, what will the exponent (11) be?

12

When the coefficient of scientific notation gets smaller, what happens to the exponent?

the exponent gets bigger (more spaces moved)

When the coefficient of scientific notation gets larger, what happens to the exponent?

the exponent gets smaller (less spaces, or negative spaces moved)

what is diameter

the distance around a circle, circumference of a circle

what is a radius

half of a diameter,

when asked for the width of a rectangle, what do you do

slash mark through the inside of the rectangle

can an x-value have two y-values?

No

which is a funtion?

bottom

why is the bottom a function and the top is not?

the bottom has all different x's, the top has repeating x's

(X,Y)

is this linear

no

is this nonlinear

yes

is this decreasing or increasing

increasing

is this linear

yes, it has a constant rate of change

what is the equation to find the rate of change for this table

is this table linear

no, the rate of change is not constant

is this linear?

yes, it has a constant rate of change

equation for a graphed slope

how to determine change of rate on a table

how to determine change of rate on a graph