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The absolute value of a number is

its distance from 0 on the nmber line

For an absolute value equation,

you must solve for both the negative value and the positive value of the number

3-x<5 and 3-x>-5

e.g. To solve |3-x|<5, set up two inequalities:

y=mx+b

Line equation

(y₂-y₁)/(x₂-x₁) or ∆y/∆x

m=(rise)/(run) is equivalent to

The midpoint of two endpoints is

the average of the x-coordinates and the average of the y-coordinates...

√(x₂-x₁)²+(y₂-y₁)²

The distance formula =

equal slope

parallel lines have

perpendicular lines have

negative reciprocal slopes

x-intercepts, roots, or zeroes

Most quadratic equations have two solutions, also known as

(x-y)(x+y)

x²-y² =

(x+y)² =

x² + 2xy + y²

(x-y)² =

x² - 2xy + y²

A quadratic function takes the form

f(x) = ax² + bx + c

up

If a > 0, the parabola opens

down

If a < 0, the parabola opens

fat

If a is a fraction, the parabola is

To quickly graph a parabola...

(a) let x=0 and find where the graph will cross the y-axis

supplementary angles =

180°, a straight line

vertical and congruent

Angles across from each other are

equal, equal

When two parallel lines are intersected by a third line, the corresponding acute angles are ________ and the corresponding obtuse angles are ________

bisects it

A line that divides an angle or another line into two equal pieces

180°

Degrees in a line

the two opposite interior angles

An exterior angle of ANY triangle is equal to the sum of the measures of

greater

In ANY triangle, a side opposite a greater angle is ______________ than a side opposite a smaller angle

also equal

In ANY triangle, sides opposite equal angles are

isosceles triangle:

a triangle with two equal sides and two corresponding equal angles

equilateral:

a triangle with three equal sides and three corresponding equal angles (each 60° in measure)

*Triangle Inequality Theorem*

every side of a triangle must be greater than the difference of the lengths of the other two sides and less than the sum of the other two sides

SIMILAR triangles have

EQUAL angles and PROPORTIONAL sides

Pythagorean triplets

3:4:5 and 5:12:13 and their multiples

x, x, x√2

The sides of a 45-45-90 degree triangle:

x, x√3, 2x

The sides of a 30-60-90 degree triangle: