#### Study sets matching "geometry theorems postulates"

#### Study sets matching "geometry theorems postulates"

Addition Propery of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a=b, then a+c=b+c

If a=b, then a-c=b-c

If a=b, then a•c=b•c

If a=b, then a÷c=b÷c

Addition Propery of Equality

If a=b, then a+c=b+c

Subtraction Property of Equality

If a=b, then a-c=b-c

if M is the midpoint of AB

through a line and a point not in the…

if two lines intersect

if BX is the bisector of angle ABC

AM = 1/2AB and MB = 1/2 AM

there is exactly one plane

exactly one plane contains the lines

measurement of angle ABX = 1/2 measurement of angle ABC

if M is the midpoint of AB

AM = 1/2AB and MB = 1/2 AM

through a line and a point not in the…

there is exactly one plane

Postulate 5

Postulate 6

Postulate 8

Postulate 9

Through any 2 points there exists exactly one line

A line contains at least 2 points

Through any 3 non-collinear points there exists exactly one p…

A plane contains at least 3 noncollinear points

Postulate 5

Through any 2 points there exists exactly one line

Postulate 6

A line contains at least 2 points

Unique line postulate

Unique plane postulate

Dimension assumption postulates

Line intersection postulate

Through any two points, there exists exactly one line

Through any three non-collinear points, there exists exactly…

-Given a line, there exists at least one point not on the lin…

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

Unique line postulate

Through any two points, there exists exactly one line

Unique plane postulate

Through any three non-collinear points, there exists exactly…

Vertical Angle Theorem

Adjacent Angle

Complementary Angle

Supplementary angle

Vertical Angles are congruent

A pair of angles in the same plane that meet the following co…

2 angles whose measures add up to 90 degrees

2 angles whose measures add up to 180 degrees

Vertical Angle Theorem

Vertical Angles are congruent

Adjacent Angle

A pair of angles in the same plane that meet the following co…

Ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

Points on a line can be matched one to one with the real numb…

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

Consider a point A on one side of lineOB. The rays of the for…

If P is in the interior of angleRST, then the measure-angleRS…

Ruler postulate

Points on a line can be matched one to one with the real numb…

Segment addition postulate

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

Segment congruence postulate

Segment addition postulate

Angle congruence postulate

Angle addition postulate

If two segements have the same length as measured by a fair r…

If point R is between points P and Q on a line then; PR + RQ…

If two angles have the same measure, then they are congruent.…

If point S is in the interior of angle PQR, then the measure…

Segment congruence postulate

If two segements have the same length as measured by a fair r…

Segment addition postulate

If point R is between points P and Q on a line then; PR + RQ…

Ruler postulate

Segment Addition postulate

Protractor postulate

Angle Addition Postulate

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

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

Consider OB and a point A on one side of OB. The rays of the…

If P is in the interior of < RST, then the measure of <RST is…

Ruler postulate

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

Segment Addition postulate

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

angle addition postulate

right angles congruence theorem

APOE

SPOE

if P is the interior of angle RST, then the measure of RST is…

all right angles are congruent

if a=b, then a+c=b+c

if a=b, then a-c=b-c

angle addition postulate

if P is the interior of angle RST, then the measure of RST is…

right angles congruence theorem

all right angles are congruent

Linear Pair Postulate

Corresponding Angles Postulate

Two Perps Theorem

Perpendicular Transversal Theorem

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

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

If two lines are perpendicular to the same line, then the lin…

If a line is perpendicular to one of two parallel lines, then…

Linear Pair Postulate

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

Corresponding Angles Postulate

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

postulate

theorem

postulate(1)

postulate(2)

a basic assumption accepted without proof

a statement that can be proved using postulates, definitions,…

a line contains at least 2 points, a plane contains at least…

through any 2 points, there is exactly one line

postulate

a basic assumption accepted without proof

theorem

a statement that can be proved using postulates, definitions,…

Linear Pair Theorem

Congruent Supplement Theorem

Right Angle Congruence Theorem

Congruent Complementary Theorem

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

If two angles are supplementary to the same angle (or to two…

All right angles are congruent

If two angles are complementary to the same angle (or two con…

Linear Pair Theorem

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

Congruent Supplement Theorem

If two angles are supplementary to the same angle (or to two…

Postulate 1-1:

Postulate 1-2:

Postulate 1-3:

Postulate 1-4:

Through any two points there is exactly one line

If two distinct lines intersect, then they intersect in exact…

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

Through any three noncollinear points there is exactly one pl…

Postulate 1-1:

Through any two points there is exactly one line

Postulate 1-2:

If two distinct lines intersect, then they intersect in exact…

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 degrees

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 degrees

Side-Side-Side Postulate... (SSS)

Side-Angle-Side Postulate... (SAS)

Angle-Side-Angle Postulate... (ASA)

Angle-Angle-Side Theorem... (AAS)

If three sides of one triangle are congruent to three of anot…

If two sides and the included angle of one triangle are congr…

If two angles and the included side of one triangle are congr…

If two angles and a non included side of one triangle are con…

Side-Side-Side Postulate... (SSS)

If three sides of one triangle are congruent to three of anot…

Side-Angle-Side Postulate... (SAS)

If two sides and the included angle of one triangle are congr…

postulate

theorem

postulate 5

postulate 6

a statement accepted without proof

a statement that requires proof

a line contains at least two points, a plane contains at leas…

through any two points there is exactly one line

postulate

a statement accepted without proof

theorem

a statement that requires proof

PBT

CPBT

RAT

≅ST

Perpendicular Bisector Theorem: If two points are equidistant…

Converse Perpendicular Bisector Theorem: If a point is on per…

Right Angle Theorem: If two angles are both congruent and sup…

Congruent Supplement Theorem: If two angles are congruent, th…

PBT

Perpendicular Bisector Theorem: If two points are equidistant…

CPBT

Converse Perpendicular Bisector Theorem: If a point is on per…

Ruler Postulate

Protractor Postulate

Angle Addition Postulate

Linear Pair Postulate

Once a coordinate system has been chosen in this way, the dis…

the measure of an angle is equal to the absolute value of the…

add two angles together, you get a bigger angle, same vertex…

If two angles form a linear pair, then they are supplementary

Ruler Postulate

Once a coordinate system has been chosen in this way, the dis…

Protractor Postulate

the measure of an angle is equal to the absolute value of the…

expansion

line

flat plane

plane intersection

Which postulate states that a line contains at least two poin…

Which postulate states that any two points in space lie in ex…

Which postulate states if two points lie in a plane, then the…

Which postulate states if two planes intersect, then their in…

expansion

Which postulate states that a line contains at least two poin…

line

Which postulate states that any two points in space lie in ex…

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Subtractive Property of equality

If point B lies on a line segment AC then AB+BC= AC

Variable that lies on the interior of angle then add the degr…

Two angles are a linear pair if the angles are adjacent and t…

States that when both sides of an equation have the same numb…

Segment Addition Postulate

If point B lies on a line segment AC then AB+BC= AC

Angle Addition Postulate

Variable that lies on the interior of angle then add the degr…

Linear Pair Postulate

Segment Addition Postulate

Angle Addition Postulate

Addition Property

If two angles form a linear pair, then they are supplementary

If you have a line made up of pieces, add the small pieces to…

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

If you add the same numbers to each side of an equation, both…

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Segment Addition Postulate

If you have a line made up of pieces, add the small pieces to…

Segment Addition Postulate

Angle Addition Postulate

Protractor Postulste

Ruler Postulate

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

If B is the Interior of < COA, then m< COB + m< BOA = m< COA

Given line AB and a point O on line AB. Consider rays OA and…

On a number line, every point can be paired with a number and…

Segment Addition Postulate

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

Angle Addition Postulate

If B is the Interior of < COA, then m< COB + m< BOA = m< COA

Congruent Supplements Theorem

Congruent Complements Theorem

Linear Pair Postulate

Vertical Angle Theorem

If two angles are supplementary to the same or congruent angl…

If two angles are complementary to the same or congruent angl…

If two angles form a linear pair, then they are supplementary

Vertical angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same or congruent angl…

Congruent Complements Theorem

If two angles are complementary to the same or congruent angl…

Postulate 1 :Ruler

Postulate 2: Segment Addition

Postulate 3: Protractor

Postulate 4: Angle Addition

1: The point on a line can be paired with the real numbers in…

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

1:How to set up a protractor... 2:How to measure an angle

Angles have to add up to 180º

Postulate 1 :Ruler

1: The point on a line can be paired with the real numbers in…

Postulate 2: Segment Addition

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

Side-Angle-Side (SAS) Congruence Postu…

Side-Side-Side (SSS) Postulate

Angle-Side-Angle (ASA) Postulate

Angle-Angle-Side (AAS) Theorem

In one triangle, if two sides and the angle between those sid…

If the three sides of one triangle are congruent to the three…

If two angles and the included side of one triangle are congr…

If two angles and a non-included side of one triangle are con…

Side-Angle-Side (SAS) Congruence Postu…

In one triangle, if two sides and the angle between those sid…

Side-Side-Side (SSS) Postulate

If the three sides of one triangle are congruent to the three…

Pythagorean Theorum

Converse of Pythagorean Theorem

If two angles are right angles then th…

If two angles are straight angles then…

A^2+B^2=C^2

If A^2+B^2=C^2 then it's a right triangle.... If it's a right tr…

If two angles have the same measure then they are congruent

If two angles have the same measure then they are congruent

Pythagorean Theorum

A^2+B^2=C^2

Converse of Pythagorean Theorem

If A^2+B^2=C^2 then it's a right triangle.... If it's a right tr…

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

The distance between points a and b is the absolute value of…

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

The measure of angle AOB is equal to the absolute value of th…

If point B is in the interior of angle COA, then the measure…

Postulate 1 (Ruler Postulate)

The distance between points a and b is the absolute value of…

Postulate 2 (Segment Addition Postulate)

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

Segment Addition Postulate

Protractor Postulate

Parallel Lines

Skew Lines

AB + BC = AC

Says that you can measure any angle

two lines that don't intersect and are coplanar

two lines that don't intersect and aren't coplanar

Segment Addition Postulate

AB + BC = AC

Protractor Postulate

Says that you can measure any angle

HL Theorem

AAS Theorem

ASA Postulate

SAS Postulate

If the two hypotenuse and a leg of one triangle are congruent…

If two angels and a non included side of one triangle are con…

If two angles and the included side of one triangle are congr…

If two sides and the included angle of one triangle are congr…

HL Theorem

If the two hypotenuse and a leg of one triangle are congruent…

AAS Theorem

If two angels and a non included side of one triangle are con…

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…

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Parallel Postulate

If B is between = A & C then, AB + BC = AC. Then B is the mid…

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

If two angles form a linear pair, then they are supplementary

If there is a line and a point not on a line, then there is e…

Segment Addition Postulate

If B is between = A & C then, AB + BC = AC. Then B is the mid…

Angle Addition Postulate

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

Corresponding angles

alternate interior angles

alternate exterior angles

consecutive interior angles

if 2 parallel lines are cut by a transversal, then the pairs…

if 2 angles lie between the 2 lines and on opposite sides of…

if 2 angles lie outside the 2 lines and on opposite sides of…

if 2 angles lie between the 2 lines and on the same side of t…

Corresponding angles

if 2 parallel lines are cut by a transversal, then the pairs…

alternate interior angles

if 2 angles lie between the 2 lines and on opposite sides of…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Consider ray OB and a point A on one side of ray OB. The rays…

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

Ruler Postulate

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

Segment Addition Postulate

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

Complementary Angles

Supplementary angles

theorem

Vertical angles

Two angles whose measures equal 90 degrees

two angles whose measures equal 180 d

a statement that can be proven

4 angles formed by intersecting lines and facing in four diff…

Complementary Angles

Two angles whose measures equal 90 degrees

Supplementary angles

two angles whose measures equal 180 d

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Line tangent to circle→Line perpendicu…

Line perpendicular to radius→line tang…

2 segments tangent to circle from same…

Arc addition postulate

If a line is tangent to a circle, then the line is perpendicu…

If a line is perpendicular to the radius, then it is tangent…

If two segments are tangent to a circle from the same externa…

the measure of an arc formed by two adjacent arcs is the sum…

Line tangent to circle→Line perpendicu…

If a line is tangent to a circle, then the line is perpendicu…

Line perpendicular to radius→line tang…

If a line is perpendicular to the radius, then it is tangent…

Parallel lines

Skew lines

Transversal

Corresponding Angles

coplanar lines that never intersect

lines that never intersect and noncoplanar

is a line in a plane that intersects at least two coplanar li…

angles in corresponding position

Parallel lines

coplanar lines that never intersect

Skew lines

lines that never intersect and noncoplanar

Segment Addition Postulate

Protractor Postulate

Parallel Lines

Skew Lines

AB + BC = AC

Says that you can measure any angle

two lines that don't intersect and are coplanar

two lines that don't intersect and aren't coplanar

Segment Addition Postulate

AB + BC = AC

Protractor Postulate

Says that you can measure any angle

Postulate 1: the distance postulate

Postulate 2: the ruler postulate

Postulate 3: the ruler placement postu…

Postulate 4: the line postulate

To every pair of different points there corresponds a unique…

the points of a line can be placed in correspondence with the…

Given two points P and Q of a line, the coordinate system can…

for every two points there is exactly one line that contains…

Postulate 1: the distance postulate

To every pair of different points there corresponds a unique…

Postulate 2: the ruler postulate

the points of a line can be placed in correspondence with the…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

pints on a line can be parried with real numbers so that any…

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

Given line AB and a point O on line AB. Consider rays OA and…

Angle 1 + Angle 2 = Angle 1+2

Ruler Postulate

pints on a line can be parried with real numbers so that any…

Segment Addition Postulate

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

Point

Line

Line Segment

Ray

Indicates a location

represented by a straight path that extends in 2 opposite dir…

Part of a line that contains 2 endpoints

Part of a line that consists of 1 endpoint and all points tha…

Point

Indicates a location

Line

represented by a straight path that extends in 2 opposite dir…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points, there is exactly one line.

Lines can only intersect at exactly one point.

Planes can only intersect at exactly one line.

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

Postulate 1-1

Through any two points, there is exactly one line.

Postulate 1-2

Lines can only intersect at exactly one point.

Ruler Postulate:

Segment Addition Postulate:

Protractor Postulate

Angle Addition Postulate:

The points on a line can be paired with the real numbers in s…

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

: On line AB of a given plane, choose any point between A and…

If point B lies in the interior of angle AOC then m angle AOB…

Ruler Postulate:

The points on a line can be paired with the real numbers in s…

Segment Addition Postulate:

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

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points, there is exactly one line.

Lines can only intersect at exactly one point.

Planes can only intersect at exactly one line.

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

Postulate 1-1

Through any two points, there is exactly one line.

Postulate 1-2

Lines can only intersect at exactly one point.

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points, there is exactly one line.

Lines can only intersect at exactly one point.

Planes can only intersect at exactly one line.

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

Postulate 1-1

Through any two points, there is exactly one line.

Postulate 1-2

Lines can only intersect at exactly one point.

Line Intersection Theorem

Linear Pair Theorem

Vertical Angles Theorem

Corresponding Angles Postulate

Two different lines intersect in at one point.

If two angels form a linear pair, then they are supplementary.

If two angles are vertical angles then they have equal measur…

If two angles have the same measure then they are parallel. I…

Line Intersection Theorem

Two different lines intersect in at one point.

Linear Pair Theorem

If two angels form a linear pair, then they are supplementary.

side XY is congruent to side XZ

Triangle Sum Thm.

Isosceles Triangle Thm.

two congruent sides

Since XY equals XZ

M<X + M<Y + M<Z = 180

base angles Z & Y are congruent so m<Z = M<Y

Isosceles Triangles have at least

side XY is congruent to side XZ

Since XY equals XZ

Triangle Sum Thm.

M<X + M<Y + M<Z = 180