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Slope-Intercept Form (most graph-able…

Point-Slope Form (to get a point and s…

Slope of Two Points

Midpoint of a Line

y=mx+b

y-y₁=m(x-x₁)

Y₂-Y₁ / X₂-X₁

(x₁+x₂ / 2) , (y₁+y₂ / 2)

Slope-Intercept Form (most graph-able…

y=mx+b

Point-Slope Form (to get a point and s…

y-y₁=m(x-x₁)

Surface Area

Lateral Area right prism

Volume of right prism

Lateral Area of regular pyramid

lateral area + 2B

Ph (Perimeter x height)

Bh (total area of Base x height)

1/2 P ℓ (ℓ = slant height)

Surface Area

lateral area + 2B

Lateral Area right prism

Ph (Perimeter x height)

Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

The distance between A and B is the absolute value of the dif…

If B is between A and C then AB+BC=AC and If AB+BC=AC then B…

If P is in the interior of angle RST then RSP+PST

If two angles form a linear pair, then they are supp.

Ruler Postulate

The distance between A and B is the absolute value of the dif…

Segment Addition Postulate

If B is between A and C then AB+BC=AC and If AB+BC=AC then B…

linear pair theorem

congruent supplements theorem

right angle congruence theorem

congruent complements theorem ,

if two angles form a linear pair then they are supplementary

if two angles are supplementary to the same angle, then the t…

all right angles are congruent

if two angles are complementary to the same angle then they a…

linear pair theorem

if two angles form a linear pair then they are supplementary

congruent supplements theorem

if two angles are supplementary to the same angle, then the t…

Two-Point Postulate

Line-Point Postulate

Line-Intersection Postulate

Three-Point Postulate

Through any 2 points there is only 1 line.

Every line contains at least 2 points.

If 2 lines intersect, then their intersection is only 1 point.

If you have 3 noncollinear points, then you have only 1 plane.

Two-Point Postulate

Through any 2 points there is only 1 line.

Line-Point Postulate

Every line contains at least 2 points.

through any two points there is exactl…

through any three noncollinear points…

if two points lie in a plane, then the…

if two lines intersect, then they inte…

(1-1-1) points/lines

(1-1-2) planes

(1-1-3) planes/lines/points

(1-1-4) lines/points

through any two points there is exactl…

(1-1-1) points/lines

through any three noncollinear points…

(1-1-2) planes

angle addition postulate

distance formula

vertical angles theorem

linear pair postulate

given two points A and C, a third point B lies on the line se…

sq root of X2 minus X1 squared plus Y2 minus Y1 squared

vertical angles are congruent

if 2 angles form a linear pair, then they are supplementary

angle addition postulate

given two points A and C, a third point B lies on the line se…

distance formula

sq root of X2 minus X1 squared plus Y2 minus Y1 squared

isosceles triangle theorem

isosceles triangle converse theorem

random theorem

corollary to theorem 4.3

if two sides of a triangle are congruent, then the angles opp…

if two angles of a triangle are congruent, then the sides opp…

the bisector of the vertex angle of an isosceles triangle is…

if a triangle is equilateral, then it is equiangular

isosceles triangle theorem

if two sides of a triangle are congruent, then the angles opp…

isosceles triangle converse theorem

if two angles of a triangle are congruent, then the sides opp…

Segment Addition Postulate... (1.2)

The Midpoint Formula... (1.3)

the distance formula... (1.3)

angle addition postulate... (1.4)

If B is between A and C, then AB + BC = AC... If AB + BC= AC, th…

[(x1 + x2)/2] , [(y₂ + y₁)/2)]

√ (x₂ - x₁)² + (y₂ - y₁)²

If P is in the interior of <RST, then m<RSP + m<PST = m<RST

Segment Addition Postulate... (1.2)

If B is between A and C, then AB + BC = AC... If AB + BC= AC, th…

The Midpoint Formula... (1.3)

[(x1 + x2)/2] , [(y₂ + y₁)/2)]

line

segment

ray

opposite rays

set of points extending in opposite directions without end; h…

part of a line that consists of two endpoints and all points…

part of a line that begins at the endpoint and extends withou…

two rays that have the same endpoint and go in opposite direc…

line

set of points extending in opposite directions without end; h…

segment

part of a line that consists of two endpoints and all points…

Post. 1-1-1

Post. 1-1-2

Post. 1-1-3

Post. 1-1-4

Through any two points there is exactly one line

Through any three noncollinear points, there is exactly one p…

If two points lie in a plane, then the line containing those…

If two lines intersect, then they intersect in exactly one po…

Post. 1-1-1

Through any two points there is exactly one line

Post. 1-1-2

Through any three noncollinear points, there is exactly one p…

Ruler Postulate

Segment Addition Postulate

Distance Formula

Protractor Postulate

The points on a line can be matched one to one with real numb…

If B is between A and C, then AB+BC=AC

The distance between A(x₁,y₁) and B(x₂,y₂) =√(x₂-x₁)+(y₂-y₁)

If point O is the center of a circle and points A and B are o…

Ruler Postulate

The points on a line can be matched one to one with real numb…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC

Transitive Property

symmetric property

reflexive property

substitution property

if a=b and b=c then a=c

if a=b then b=a

for any real number a, a=a

if a=b then a can be substituted for binary equation/expression

Transitive Property

if a=b and b=c then a=c

symmetric property

if a=b then b=a

segment

ray

opposite rays

collinear

consists of endpoints and all points on the line between line…

consists of initial point and all points on the line AB that…

two rays that are collinear and share the same initial point

points, segments, or rays that lie on the same line

segment

consists of endpoints and all points on the line between line…

ray

consists of initial point and all points on the line AB that…

Point

Line

Segment

Ray

A dot represented by a letter.

Two points determine a line. A line is never ending.

Two points determine a segment. A segment has a definite end…

Two points determine a ray. A ray has one definite end and a…

Point

A dot represented by a letter.

Line

Two points determine a line. A line is never ending.

Postulate - 2.1

Postulate - 2.2

Postulate - 2.3

Postulate - 2.4

Through any two points, there is exactly one line

Through any three non collinear points, there is exactly one…

A line contains at least two points

A plane contains at least three non collinear points

Postulate - 2.1

Through any two points, there is exactly one line

Postulate - 2.2

Through any three non collinear points, there is exactly one…

Postulate

Ruler Postulate

Segment Addition Postulate

Midpoint Formula

Something we believe to be true but cannot prove.

The distance between two points is the absolute value of the…

If a point is between to other points then they MUST be colli…

M = {(x2+x1)/2 , (y2+y1)/2} or reverse {(x1+x2)/2 , (y1+y2)/2}

Postulate

Something we believe to be true but cannot prove.

Ruler Postulate

The distance between two points is the absolute value of the…

point

line

plane

segment

names a location and has no size. it's represented by a dot

a straight path that has no thickness and extends forever

a flat surface that has no thickness and extends forever

part of a line consisting of two points and all points betwee…

point

names a location and has no size. it's represented by a dot

line

a straight path that has no thickness and extends forever

Definition of Opposite Rays

Definition of Congruent Segments

segment addition postulate

Definition of midpoint

Any two rays joined with an endpoint always have an angle bet…

congruent means exactly equal in size and shape. Congruent Se…

If a point B lies on a line segment AC then segment AB+segmen…

The point halfway between the two endpoints of a line segment.

Definition of Opposite Rays

Any two rays joined with an endpoint always have an angle bet…

Definition of Congruent Segments

congruent means exactly equal in size and shape. Congruent Se…

Midsegment Theorem

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Concurrency of Perpendicular Bisectors…

The segment connecting the midpoints of two sides of a triang…

In a plane, if a point is on the perpendicular bisector of a…

In a plane, if a point is equidistant from the endpoints of a…

The perpendicular bisectors of a triangle intersect at a poin…

Midsegment Theorem

The segment connecting the midpoints of two sides of a triang…

Perpendicular Bisector Theorem

In a plane, if a point is on the perpendicular bisector of a…

Midsegment Theorem

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Concurrency of Perpendicular Bisectors…

The segment connecting the midpoints of two sides of a triang…

In a plane, if a point is on the perpendicular bisector of a…

In a plane, if a point is equidistant from the endpoints of a…

The perpendicular bisectors of a triangle intersect at a poin…

Midsegment Theorem

The segment connecting the midpoints of two sides of a triang…

Perpendicular Bisector Theorem

In a plane, if a point is on the perpendicular bisector of a…

Collinear Points

Noncollinear Points

Coplanar Points

Noncoplanar

Points that are all in one line

Points that are not in one line

Points that are in one plane

Points that are in multiple planes

Collinear Points

Points that are all in one line

Noncollinear Points

Points that are not in one line

Reflexive

Symmetric

Transitive

Segment Addition Postulate

Line segment AB is congruent to line segment CD

If line segment AB is congruent to line segment CD, then line…

If line segment AB is congruent to line segment CD, and line…

Two segments of a line added together to get the length of th…

Reflexive

Line segment AB is congruent to line segment CD

Symmetric

If line segment AB is congruent to line segment CD, then line…

Congruent Segments

Congruent Angles

Midpoint

Segment Bisector

Segments whose lengths are equal.

Angles whose measures are equal.

Point that divides a segment into 2 congruent segments.

Line (or part of a line) that intersects the segment at its m…

Congruent Segments

Segments whose lengths are equal.

Congruent Angles

Angles whose measures are equal.

Def. of congruent

Def. of midpoint

Segment bisector

Def. of acute

When two angles or lines are equal size. ... Ex. If line AD=BC t…

Divides a segment into two congruent segments... Ex. If f is the…

Point, line, segment, Ray, or plane, that divides a segment i…

angle less than 90*

Def. of congruent

When two angles or lines are equal size. ... Ex. If line AD=BC t…

Def. of midpoint

Divides a segment into two congruent segments... Ex. If f is the…

equilateral triangle

equiangular triangle

acute triangle

scalene triangle

a triangle with all sides congruent

a triangle with all angles congruent

a triangle in which all of the angles are acute angles

a triangle with no two sides congurent

equilateral triangle

a triangle with all sides congruent

equiangular triangle

a triangle with all angles congruent

triangle

Classifying Triangles

interior angles

exterior angles

polygon with 3 sides

>by sides: ... ~scalene: no congruent sides ... ~isosceles: two con…

the angles inside of the polygon (triangle)

form linear pairs with interior angles on the outside of the…

triangle

polygon with 3 sides

Classifying Triangles

>by sides: ... ~scalene: no congruent sides ... ~isosceles: two con…

parallel lines

skew lines

parallel planes

transversal

lines in the same plane that do not intersect

lines that are not coplanar and do not intersect

planes that do not intersect

a line that intersects two coplanar lines at two different po…

parallel lines

lines in the same plane that do not intersect

skew lines

lines that are not coplanar and do not intersect

midsegment of a triangle

coordinate proof

perpendicular bisector

equidistant

a segment that connects the midpoints of the two sides of the…

a type of proof that involves placing geometric figures in a…

a segment, ray, line, or plane that is perpendicular to a seg…

the same distance

midsegment of a triangle

a segment that connects the midpoints of the two sides of the…

coordinate proof

a type of proof that involves placing geometric figures in a…

Pythagorean Triple

Geometric Mean

Trigonometric Ratio

Tangent

A Pythagorean triple is a set of three positive integers a,b,…

For positive numbers a and b, the positive number x such that…

A ratio of two sides of a right triangle

A line or a plane that touches a curve or a surface at a poin…

Pythagorean Triple

A Pythagorean triple is a set of three positive integers a,b,…

Geometric Mean

For positive numbers a and b, the positive number x such that…

The "Undefined Terms of Geometry"...

point

line

plane

point, line, plane

a location in space represented by a dot and usually assigned…

a straight path that extends without end in opposite directions

a flat surface that extends forever

The "Undefined Terms of Geometry"...

point, line, plane

point

a location in space represented by a dot and usually assigned…

1-1

1-2

1-3

1-4

Through any two points there in exactly one line

Two distinct lines intersect in exactly one point

If two distinct planes intersect, then they intersect in exac…

Through any non-collinear points, there is exactly one plane

1-1

Through any two points there in exactly one line

1-2

Two distinct lines intersect in exactly one point

The "Undefined Terms of Geometry"...

point

line

plane

point, line, plane

a location in space represented by a dot and usually assigned…

a straight path that extends without end in opposite directions

a flat surface that extends forever

The "Undefined Terms of Geometry"...

point, line, plane

point

a location in space represented by a dot and usually assigned…

The "Undefined Terms of Geometry"...

point

line

plane

point, line, plane

a location in space represented by a dot and usually assigned…

a straight path that extends without end in opposite directions

a flat surface that extends forever

The "Undefined Terms of Geometry"...

point, line, plane

point

a location in space represented by a dot and usually assigned…

Exterior angle inequality theorem

Inverse

Contrapositive

Theorem 6-2

the measure of an exterior angle of a triangle is greater tha…

if not a, then not b... Logically equivalent with Converse

if not b, then not a... logically equivalent with conditional

If one side of a triangle is longer than a second side, then…

Exterior angle inequality theorem

the measure of an exterior angle of a triangle is greater tha…

Inverse

if not a, then not b... Logically equivalent with Converse

Point

Line

Plane

Space

Dot, has no size, named using capital letters, just posistion

Represented with arrowheads, infinite, no thickness

No thickness, infinite in all directions

Set of all points

Point

Dot, has no size, named using capital letters, just posistion

Line

Represented with arrowheads, infinite, no thickness

Congruent Segments

Congruent Angles

Midpoint

Segment bisector

Segments whose lengths are equal

Angles whose measures are equal

Point that divides a segment into 2 congruent segments

Line (or part of a line) that intersects the segments at its…

Congruent Segments

Segments whose lengths are equal

Congruent Angles

Angles whose measures are equal

Non-Vertical Lines Parallel Line Theorem

Non-Vertical Lines Perpendicular Line…

Segment Addition Postulate

Angle Addition Postulate

Two non-vertical are parallel lines if and only if their slop…

Two non-vertical lines are perpendicular if and only if the p…

Let A, B, & C, be collinear points. If B is between A & C, th…

If Point S is in the interior of Angle PQR, then m∠PQS + m∠SQ…

Non-Vertical Lines Parallel Line Theorem

Two non-vertical are parallel lines if and only if their slop…

Non-Vertical Lines Perpendicular Line…

Two non-vertical lines are perpendicular if and only if the p…

Reflexive

Symmetric

Transitive

Segment Addition Postulate

Line segment AB is congruent to line segment CD

If line segment AB is congruent to line segment CD, then line…

If line segment AB is congruent to line segment CD, and line…

Two segments of a line added together to get the length of th…

Reflexive

Line segment AB is congruent to line segment CD

Symmetric

If line segment AB is congruent to line segment CD, then line…

Def. of congruent

Def. of midpoint

Segment bisector

Def. of angle bisector

When two angles or lines are equal size. ... Ex. If line AD=BC t…

Divides a segment into two congruent segments... Ex. If f is the…

Point, line, segment, Ray, or plane, that divides a segment i…

Ray that divides an angle into two congruent adjacent angles…

Def. of congruent

When two angles or lines are equal size. ... Ex. If line AD=BC t…

Def. of midpoint

Divides a segment into two congruent segments... Ex. If f is the…

Congruent Segments

Congruent Angles

Midpoint

Segment bisector

Segments whose length are equal

Angles whose measures are equal

Point that divides a segment into 2 congruent segments

Line (or part of a line) that intersects the segment at its m…

Congruent Segments

Segments whose length are equal

Congruent Angles

Angles whose measures are equal

congruent segments

congruent angles

midpoint

segment bisector

two segments that have the same length

two angles that have the same measure

the point that divides a segment into two congruent segments

a line, ray, or segment that divides a segment into two congr…

congruent segments

two segments that have the same length

congruent angles

two angles that have the same measure