Midpoint Formula

(x₁ + x₂  ,  y₁ + y₂)

2               2

Distance Formula

√(x₂-x₁)² + (y₂ - y₁)²

Altitude Proportion

                 altitude             =      part of hypotenuse

          part of hypotenuse                   altitude   

Leg Proportion

                Leg            =      Part of hypotenuse

         adjacent part of                    Leg

            hypotenuse

Volume of a Rectangular Prism

V = l w h

Volume of a Triangular Prism

V =  l w h

    2

Volume of a Cylinder

V = π r² h

Volume of a Cone

V = 1/3 π r² h

Volume of a Pyramid

V = 1/3 l w h

Interior Angle Sum of a Polygon

(n - 2)*180

n = number of sides

Measure of One Interior Angle in a Polygon

(n - 2)*180

n

Exterior Angle Sum

ALWAYS 360°

Measure of One Exterior Angle in a Polygon

360

n

How do you write the contrapositive?

Switch and Negate the statement

How do you write the inverse?

Negate both parts of the statement

How do you write the converse?

Switch the two parts of the statement

How do you write a logically equivalent statement?

Same as contrapositive

Switch and negate the statement

How do you know if two lines are parallel?

They have the same SLOPE.

How do you know if lines are perpendicular?

The slopes are negative reciprocals of each other.

1/2 --> -2

4 --> -1/4

-3/2 --> 2/3

What is the angle sum of a triangle?

180°

What is the rule for reflecting over the y-axis?

Change the sign of x

(x, y) --> (-x, y)

What is the rule for reflecting over the x axis?

Change the sign of y

(x, y) --> (x , -y)

What is the rule for reflecting over the line y = x?

Switch x and y

(x, y) --> (y , x)

What is the rule for tranlating a figure T_{(4, -2)}

Add 4 to the x coordinate and add -2 to the y coordinate

What is the rule for rotating 90°?

Switch x and y then change the sign of the new x

(x, y) --> (-y, x)

What is the rule for rotating 180°?

Change the sign of x and y

(x, y) --> (-x, -y)

What is the rule for dilating D₂?

Multiply x and y by 2

(x, y) -->  (2x, 2y)

Which transformation is not an isometry?

DILATION

What is an isometry?

A transformation where the preimage and image are congruent.

Which transformation does not persreve orientation?

REFLECTIONS

What are the 3 ways that do NOT prove triangles congruent?

AAA, ASS, and SSA

What are the 5 ways to prove triangles cognruent?

SSS, SAS, ASA, AAS and HL

What are the 3 ways to prove triangles similar?

AA, SSS and SAS

(where the angles are congruent and

the sides are proportional)

When is a conjunction true? 

(Statment with AND)

When is a disjunction true?

(Statement with OR)

Points or lines on the same plane

Parallel lines are coplanar

Relationship between the side lengths of triangles

(Triangle inequality)

The smaller part of the median is 1/3 the entire length

The larger part is double the smaller part

Corresponding parts of congruent triangles are congruent

does NOT prove triangles congruent

Proves correponding angles and sides of triangles are congruent

Opposide sides parallel

Opposite angles congruent

Opposide sides congruent

Diagnoals bisect each other

Side by side angles are supplementary (180)

Diagonals are NOT congruent

4 congruent sides

Opposite angles congruent

Opposite sides parallel and congruent

Diagonals bisect each other

Diagonals are PERPENDICULAR

Angles are bisected by diagonals

Oppside sides congruent and parallel

All angles are 90°

Diagonals bisect each other

Diagonals are congruent

All sides are congruent

All angles are 90°

Diagonals are congruent

Diagonals are perpendicular

Diagonals bisect each other