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Postulate 5

Postulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line

Line contains at least two points

If two lines intersect, their intersection is exactly one point

Through any three non collinear points there exists one plane

Postulate 5

Through any two points there exists exactly one line

Postulate 6

Line contains at least two points

Circumcenter thm

The circumcenter

Incenter thm

The incenter

equal distant to the VERTICIES of a triangle

Is the point where 3 PERPENDICULAR BISECTORS of a triangle in…

Equidistant from the SIDES of a triangle

Is is the point where the ANGLE BISECTORS of a triangle inter…

Circumcenter thm

equal distant to the VERTICIES of a triangle

The circumcenter

Is the point where 3 PERPENDICULAR BISECTORS of a triangle in…

1. Annulus

2. Apothem

3. Area of a Parallelogram

4. Area of a Square

A ring-shaped region bound by two concentric circles (they ha…

The distance from the side of a regular polygon to the center…

bh

bh ... or... s squared (s=side length)

1. Annulus

A ring-shaped region bound by two concentric circles (they ha…

2. Apothem

The distance from the side of a regular polygon to the center…

isosceles triangle

point slope form

slope intercept form

parallel lines

two sides congruent ... base angles same... if equilateral, then it…

Y-Y1=M(X-X1)

Y=Mx+B

same slope different Y intercept

isosceles triangle

two sides congruent ... base angles same... if equilateral, then it…

point slope form

Y-Y1=M(X-X1)

acute angle

adjacent angles

angle

area

an angle greater than 0 and less than 90

two angles in the same place with a common vertex and a commo…

a figure formed by two rays with a common endpoint

the number of non overlapping unit square of a given size tha…

acute angle

an angle greater than 0 and less than 90

adjacent angles

two angles in the same place with a common vertex and a commo…

POINT

LINE

Line Segment

Ray

A location and has no size. It is represented by a dot.

An object with no width that extends forever in both directio…

A part of a line consisting of two end points in between.

Part of a line consisting one end point extending forever in…

POINT

A location and has no size. It is represented by a dot.

LINE

An object with no width that extends forever in both directio…

Point, Line, and Plane

Point

Line

Plane

the three undefined terms in geometry.

has no dimension and is represented by a dot with a capital l…

has one dimension and is a set of points that extend infinite…

has two dimensions and extends infinitely in all directions.

Point, Line, and Plane

the three undefined terms in geometry.

Point

has no dimension and is represented by a dot with a capital l…

Reflection

Translation

Rotation

Symmetry

Flips a line over a line of reflection (same distance)

Sliding along a vector <a,b> by adding a to X and b to y

Turns around center of rotation ... New is same distance from ce…

Shape is symmetric if a transformation = identical image

Reflection

Flips a line over a line of reflection (same distance)

Translation

Sliding along a vector <a,b> by adding a to X and b to y

Corresponding angles

Alternate interior angles

Complementary angles

Linear pair

Share same position at each intersection across || lines... Equal

Angles formed on opposite sides of transversal and inside the…

2 angles=90 degrees

A pair of adjacent angles

Corresponding angles

Share same position at each intersection across || lines... Equal

Alternate interior angles

Angles formed on opposite sides of transversal and inside the…

Segment Addition Postulate

Angle Addition Postulate

Substitution Property

Congruence

If points A, B, and C are collinear and B is between A and C,…

If point B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m…

If b = c, then c can replace b in any expression.

Segments or angles that has the same measure.

Segment Addition Postulate

If points A, B, and C are collinear and B is between A and C,…

Angle Addition Postulate

If point B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m…

Conjecture

Inductive reasoning

Conditional statement

Conclusion of statement

A statement you believe to be true

Making a conjecture based on pattern or example ( specific to…

A logical statement in form of "if...then"

Comes after. The then

Conjecture

A statement you believe to be true

Inductive reasoning

Making a conjecture based on pattern or example ( specific to…

circumcenter

incenter

median

centroid

the intersection of the perpendicular bisectors. It will make…

the intersection of the angle bisectors. It will make a circl…

segment that runs from a midpoint to the opposite vertex

intersection of the medians

circumcenter

the intersection of the perpendicular bisectors. It will make…

incenter

the intersection of the angle bisectors. It will make a circl…

Polygon Interior Angle Sum

Looking for 1 Interior Angle

Polygon EXT angles sum

Parallelogram (6.3)

The sum of the interior angles measures "180(n-2)"

"180(n-2)/n"

The sum of the exterior angles will always be "360"

Opposite sides are congruent

Polygon Interior Angle Sum

The sum of the interior angles measures "180(n-2)"

Looking for 1 Interior Angle

"180(n-2)/n"

Inductive Reasoning

Conjecture

Counter example

Conditional Statement

Type of reasoning that looks for a pattern to reach a conclus…

A conclusion reached by inductive reasoning (it is proven and…

A specific case used to prove a conjecture is false; the conc…

A logical statement that has 2 parts called a hypothesis and…

Inductive Reasoning

Type of reasoning that looks for a pattern to reach a conclus…

Conjecture

A conclusion reached by inductive reasoning (it is proven and…

Circum-center of a triangle

Circumscribed about

Concurrent

In-center of a triangle

The point of currency of the perpendicular bisector of a tria…

A circle is circumscribed about a polygon if the vertices of…

When three or more lines intersect at one point,they are conc…

The point of concurrency of the angle bisectors of a triangle.

Circum-center of a triangle

The point of currency of the perpendicular bisector of a tria…

Circumscribed about

A circle is circumscribed about a polygon if the vertices of…

Annulus

Apothem

Composite Figure

Great Circle of a Sphere

A ring-shaped object, structure, or region.

A line from the center of a regular polygon at right angles t…

A figure (or shape) that can be divided into more than one of…

A great circle, also known as an orthodrome or Riemannian cir…

Annulus

A ring-shaped object, structure, or region.

Apothem

A line from the center of a regular polygon at right angles t…

Point

Line

collinear points

plane

A point has no dimension, but can be visualized as a specific…

A line is made up of an infinite number of points that extend…

points that are located on the same line

a flat surface with infinite length and width, but no depth.…

Point

A point has no dimension, but can be visualized as a specific…

Line

A line is made up of an infinite number of points that extend…

Parallel lines

Skew lines

Parallel planes

Transversal

2 lines that do not intersect and are coplanar

2 lines that do not intersect and are not coplanar

2 planes that do not intersect

A line that intersects two or more coplanar lines at differen…

Parallel lines

2 lines that do not intersect and are coplanar

Skew lines

2 lines that do not intersect and are not coplanar

If B is between A and C, then

If P is in the interior of ∠RST, then

If B is the midpoint of AC, then

If two angles are vertical, then

Segment Addition Postulate... AB+BC=AC

Angle Addition Postulate... m∠RSP + m∠PST = m∠RST

...

they are formed by 2 pairs of opposite rays.

If B is between A and C, then

Segment Addition Postulate... AB+BC=AC

If P is in the interior of ∠RST, then

Angle Addition Postulate... m∠RSP + m∠PST = m∠RST

Quadrilateral

Square

Rectangle

Perimeter

A 4 sided figure or having 4 straight sides.

A plane figure with 4 equal straight sides and 4 right angles.

A plane figure with 4 straight sides and 4 right angles. Oppo…

Distance around a figure

Quadrilateral

A 4 sided figure or having 4 straight sides.

Square

A plane figure with 4 equal straight sides and 4 right angles.

angle of rotation

center of dilation

center of rotation

composition of transformations

the positive number of degrees that a figure rotates

See dilation

See rotation

A composition of transformations is a combination of two or m…

angle of rotation

the positive number of degrees that a figure rotates

center of dilation

See dilation

Angle

Parallel lines

Congruent

Collinear

A figure formed by two rays with a common endpoint

Two lines that could go in forever and never meet.

Same size, same shape.

Three points that lie on the same line.

Angle

A figure formed by two rays with a common endpoint

Parallel lines

Two lines that could go in forever and never meet.

Inductive reasoning

Conjecture

What is it called when 2 statements ar…

A compound statement using the word an…

Reasoning that uses numbers of specfic examples to to arrive…

A statement or conclusion drawn from inductive reasoning

A compound statement

Conjunction

Inductive reasoning

Reasoning that uses numbers of specfic examples to to arrive…

Conjecture

A statement or conclusion drawn from inductive reasoning

Undefined terms

Inductive reasoningg

Deductive reasoning

Law of detachment

Terms that cannot be defined with simpler terms (points, line…

Using a pattern to form a conjecture

Using rules to prove a conjecture

p->q... p; therefore q

Undefined terms

Terms that cannot be defined with simpler terms (points, line…

Inductive reasoningg

Using a pattern to form a conjecture

TRANSFORMATION

DEGREE OF ROTATION

DILATION

POINT OF ROTATION

general term for 4 specific ways to manipulate the shape of a…

measure of degree an angle is fixated around a point.

produces an image that is the same shape, but a different size.

see "degree of rotation"

TRANSFORMATION

general term for 4 specific ways to manipulate the shape of a…

DEGREE OF ROTATION

measure of degree an angle is fixated around a point.

Collinear

Ray

Postulate

Segment

Points that lie on the same line

A point with a line extending forever in one direction

A statement that is accepted as true

A line with two definite end points

Collinear

Points that lie on the same line

Ray

A point with a line extending forever in one direction

Rhombus

Rectangle

Square

Trapezoid

~ all properties of a parallelogram... ~ all sides are congruent…

~ all properties of a parallelogram... ~ all angles are right an…

~ all properties of a parallelogram... ~ all properties of a rho…

~ 1 pair of opposite sides parallel (definition)... ~ 2 pairs co…

Rhombus

~ all properties of a parallelogram... ~ all sides are congruent…

Rectangle

~ all properties of a parallelogram... ~ all angles are right an…

What is the radian exact for 360 degre…

What does the Greek letter theta mean?

What is the coordinate exact for 330 d…

What are the trig forms of the coordin…

2 pi

Angle

Square root of 3/2, 1/2

Cos theta, sin theta

What is the radian exact for 360 degre…

2 pi

What does the Greek letter theta mean?

Angle

triangle sum theorem

exterior angle theorem

third angle theorem

SSS postulate

the sum of the measures of the interior angles of a triangle…

the measure of the exterior angle of a triangle is equal to t…

if two angles of a triangle are congruent to two angles of an…

if the three sides of a triangle are congruent to the three s…

triangle sum theorem

the sum of the measures of the interior angles of a triangle…

exterior angle theorem

the measure of the exterior angle of a triangle is equal to t…

postulate 5

postulate 6

postulate 7

postulate 8

through any two points there exists exactly one line

aa line consists at least 2 points

if two lines intersect, then there intersection is exactly on…

through any three noncollinear points there exists exactly on…

postulate 5

through any two points there exists exactly one line

postulate 6

aa line consists at least 2 points

Point

Line

Collinear Points

Plane

An exact location, no size, only position

Straight, no thickness, extends in both directions infinitely

Two or more points on the same line

A flat surface with no thickness

Point

An exact location, no size, only position

Line

Straight, no thickness, extends in both directions infinitely

ray

line segment

congruent segments

midpoint

part of a line that consists of an endpoint and all points on…

a line consisting of two endpoints.

line segments that have the same length.

a point that divides, or bisects, a segment into two congruen…

ray

part of a line that consists of an endpoint and all points on…

line segment

a line consisting of two endpoints.

<ABC is a right angle.

<CDE is a straight angle.

<1 and <2 are complementary angles.

<3 and <4 are supplementary angles.

m<ABC = 90; Definition of a right angle.

m<CDE = 180; Definition of a straight angle.

m<1 + m<2 = 90; Definition of complementary angles.

m<3 + m<4 = 180; Definition of supplementary angles.

<ABC is a right angle.

m<ABC = 90; Definition of a right angle.

<CDE is a straight angle.

m<CDE = 180; Definition of a straight angle.