#### Study sets matching "math geometry vocab theorems postulates formulas"

#### Study sets matching "math geometry vocab theorems postulates formulas"

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)

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…

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…

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)

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

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.

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

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)]

Segment Addition postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same-Side Interior Angles Theorem

AB+BC=AC

If two parallel lines are cut by a transversal then the pair…

If two parallel lines are cut by a transversal then the pair…

If two parallel lines are cut by a transversal then the pair…

Segment Addition postulate

AB+BC=AC

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal then the pair…

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

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…

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…

converse of the Alternate Interior Ang…

converse of the same-side interior ang…

converse of the alternate exterior ang…

converse of the corresponding angles t…

If two lines and a transversal form alternate interior angles…

If two lines and a transversal form same-side interior angles…

if two lines and a transversal form alternate exterior angles…

if two lines and a transversal form corresponding angles that…

converse of the Alternate Interior Ang…

If two lines and a transversal form alternate interior angles…

converse of the same-side interior ang…

If two lines and a transversal form same-side interior angles…

1-1-1

1-1-2

1-1-3

1-1-4

through any two points there is exactly one line

through any three non collinear 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 point

1-1-1

through any two points there is exactly one line

1-1-2

through any three non collinear points there is exactly one p…

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…

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.

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

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…

point

line

collinear points

plane

a location with no dimensions

a one dimensional connection between two points that extends…

two points that are on the same line

a two dimensional extension that als extends forever

point

a location with no dimensions

line

a one dimensional connection between two points that extends…

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…

Inductive reasoning`

Conjecture

Counterexample

Point

Reasoning that is based on patterns you observe

A conclusion you reach using inductive reasoning

An example for which the conjecture is incorrect

A location named by a capital

Inductive reasoning`

Reasoning that is based on patterns you observe

Conjecture

A conclusion you reach using inductive reasoning

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…

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

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…

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…

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

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…

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…

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

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…

**SEGMENT ADDITION POSTULATE**

**MIDPOINT THEOREM**

**ANGLE ADDITION POSTULATE**

**ANGLE BISECTOR THEOREM**

you can find the length of a segment by adding together two s…

If M is the midpoint of segment AB, then seg AM = ½AB and seg…

m<AOB + m<BOC = m<AOC... - The two angles must have a common si…

If ray BX is the bisector of <ABC, then m<ABX = ½m<ABC and m<…

**SEGMENT ADDITION POSTULATE**

you can find the length of a segment by adding together two s…

**MIDPOINT THEOREM**

If M is the midpoint of segment AB, then seg AM = ½AB and seg…

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.

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

Quadrilateral

Parallelogram

5 Ways to Prove a Quadrilateral is als…

Symbol for Parallel

A polygon with 4 sides

A quadrilateral with 2 pairs of opposite sides that are //

1. Both Pairs of Opposite Sides are //... 2. Both Pairs of Oppos…

//

Quadrilateral

A polygon with 4 sides

Parallelogram

A quadrilateral with 2 pairs of opposite sides that are //

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…

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…

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…