# Math Praxis

## 68 terms

side-side-side

side-angle-side

angle-side-angle

### AAS

2 angles and non-included side

### SSA/AAA

The two postulates that do not work

### Isosceles Triangle Theorem

If 2 sides of a triangle are congruent then the angles opposite those sides are congruent

hyp = Root2 * s

### 30-60-90

short-S
longer- Root 3 * s
Hyp -2s

### Induction

Look for a pattern of what you know and make a conjecture about what you don't know

### Combinations

Unique grouping of objects

F(t) = Ao * b^rt
Ao = initial
r-growth rate
t-time

### Deduction

Use rules that are certainly true and use them to find particular facts
conditional statements are at the foundation of deduction

90º 0,1

### pi/3

60º 1/2, root 3/2

### pi/4

45º, root2/2, root2/2

### pi/6

30º, root3/2, 1/2

1,0

### SOH

Sine = opposite/hypotenuse

=sine/cosine

1/sinº

1/cosine º

cosine/sine

### Reflexive

Every triangle is congruent to itself

### Symmetric

If ABC ~ DEF, then DEF ~ ABC

### Transitive

If ABC ~ DEF, and DEF ~ GHI, then ABC ~ GHI

### CPCTC

corresponding parts of congruent triangles are congruent

### Transversal

Line that crosses two parallel lines:
1) Corresponding angles are congruent
2) Alternate interior angles are congruent
3) Consecutive interior angles are supplementary

### Syllogism

If a, then b (a=>b
If b, then c b=>c
You can conclude If a, then c a=>c

### Rhombus

4 congruent sides
Diagonals are perpendicular
Diagonals bisect pair of angles

### Supplementary

Linear pair; 180º straight angle

### Multiplication Law of exponents

b^n * b^m = b^(n+m)

### Division law of exponents

(b^n)/(b^m) = b^(n-m)

(b^n)^m = b^n*m

### principal square root

(b^1/2)^2 = b. b^1/2 is the principal square root

the number underneath the principal square root

### domain

The set of all values that a function can take as inputs. (all numbers that can be substituted for the independent variable)

### range

The set of all values that a function will return as outputs

### Distance formula

Square root: (x2-x1)^2 + (y2-y1)^2

### Perpendicular Lines

The slopes of perpendicular lines are negative reciprocals

y=mx+b.

### Point-Slope Equation

y-yo = m(x-xo) where m is the slope of the line and (xo, yo) is a point of line

### Composite

An integer that can be factored

### Zero Product Rule

If AxB = 0, then either A = 0 or B=0. This helps solve quadratic equations

### Roots

Of a polynomial is where the value = 0. (zeroes); Roots are where polynomials cross the x-axis...If b is a root then (x-b) = a factor

### Discriminant

The number under the radicand sign of the quadratic formula (b^2 - 4ac); A + = 2 real solutions, A discriminant of 0 = one real solution; A - discriminant = 2 complex solutions

### Complex number

Numbers in the a + bi form where a and b are real numbers and i is imaginary...negative radicands

### Imaginary number

bi, where b is a real # and i is imaginary...negative radicands

ax^2 + bx + c

### Difference of squares

(A^2 - B^2) = (A+B)(A-B)

### Perfect square trinomial

where factor has a single repeated factor

### Difference of 2 cubes

A^3 - B^3 = (A-B)(A^2 + AB + B^2)

### Sum of 2 cubes

A^3 + B^3 = (A+B)(A^2 - AB + B^2)

An expression that contains a square root sign

Must have the same degree and radicand to be able to be added and subtracted

### Rationalizing the denominator

When the denominator contains a radical. Simplify by multiplying by a helpful form of 1 where only the numerator has a radical...if there is more than one term in the denominator then multiply by the conjugate of the denominator (a + b) = conjugate = (a-b)

### Converse

Dealing with conditional statements:
From a=> f becomes f =>a

### Inverse

Dealing with conditional statements:
From a=> f becomes not a => not f

### Contrapositive

Dealing with conditional statements;
From a => f becomes not f => not a

### Rays

Start at one endpoint and goes towards the other point endlessly...has a one sided arrow; Rays make up the sides of angles

### Lines

Have no width and extend forever in both directions...has a bar with two-sided arrow above it

### Vertical Angle Theorem

Vertical angles are always congruent

### Standard Equation of a circle

Centered at a point (h,v) with radius r= (x-h)^2 + (y-v)^2 = r^2

### Triangle Inequality Theorem

The sum of the two shorter lengths will always be greater than the length of the third side

A(t) = P*e^rt

### Arithmetic Sequences

An= a1 + (n-1) * d

### Geometric Sequences

An = a1 * r^(n-1)

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