# Study sets matching "geometry properties corollaries"

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Postulate

Basic Postulates of Geometry

Angle Addition Postulate

Linear Pair Postulate

"Common sense rules" based on other definitions.

The intersection of two lines is a point.... How many points det…

If an angle is split by another ray, then the two parts add up…

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

Postulate

"Common sense rules" based on other definitions.

Basic Postulates of Geometry

The intersection of two lines is a point.... How many points det…

(Postulate 1)The Ruler Postulate

(Postulate 2) The Segment Addition Post…

(Postulate 3) The Protractor Postulate

(Postulate 4) The Angle Addition Postul…

On a number line, the distance between 2 pts. can be determine…

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

Angles have a measure between 0 degrees (Exclusive) and 180 de…

If point P is in the interior of ∠ABC, then ... m∠ABP + m∠PBC = m…

(Postulate 1)The Ruler Postulate

On a number line, the distance between 2 pts. can be determine…

(Postulate 2) The Segment Addition Post…

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

Addition Property of Inequality (API)

Multiplication Property of Inequality (…

Division Property of Inequality (DPI)

Transitive Property of Inequality (TPI)

If a>b and c≥d, then a+c>b+d

If a>b and c>0, then ac>bc... and... If a>b and c<0, then ac<bc

If a>b and c>0, then a/c>b/c... and... If a>b and c<0, then a/c<b/c

If a>b and b>c, then a>c

Addition Property of Inequality (API)

If a>b and c≥d, then a+c>b+d

Multiplication Property of Inequality (…

If a>b and c>0, then ac>bc... and... If a>b and c<0, then ac<bc

Point

Line

Line Segment

Plane

Does not have any size or shape; Used to identify a location

Extends forever in two directtions; There is no infinite numbe…

A line connected by two endpoints

Extends forever with no thickness; Must have at least 3 points

Point

Does not have any size or shape; Used to identify a location

Line

Extends forever in two directtions; There is no infinite numbe…

If point D lies in between angle ABC, t…

If point B lies between A and C, then A…

AB=AB

If a=b then a+c=a+b, c-a=c-b, c/a=c/b,…

Angle Addition Postulate (both parts)

Segment Addition Postulate

Reflexive Property

Addition/Subtraction/Division/Multiplication Property of Equal…

If point D lies in between angle ABC, t…

Angle Addition Postulate (both parts)

If point B lies between A and C, then A…

Segment Addition Postulate

if 2 angles of one triangle are congrue…

____ the third angles are congeuent

what are the measures of the angles of…

how many obtuse or right angles can be…

the third angles are congruent

if 2 angles of one triangle are congruent to two angles of ano…

each angle of an equiangular triangle has measure 60

in a triangle, there can be at most one right angle or obtuse…

if 2 angles of one triangle are congrue…

the third angles are congruent

____ the third angles are congeuent

if 2 angles of one triangle are congruent to two angles of ano…

segment addition postulate (2)

angle addition postulate (4)

postulate 5

postulate 6

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

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

through any two points there exists exactly one line

a line contains at least two points

segment addition postulate (2)

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

angle addition postulate (4)

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

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 pl…

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 pl…

Determinance Postulate 1

Ruler Postulate

Segment Addition Postulate

Intersection Postulate 1

Through two points, there is exactly one line

The measure of any line segment is a unique positive number

If X is a point on line segment AB, and is between points A an…

If two lines intersect, their intersection is exactly one point

Determinance Postulate 1

Through two points, there is exactly one line

Ruler Postulate

The measure of any line segment is a unique positive number

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 3: Protractor Postulate

Postulate 4: Angle Addition Postulate

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

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

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior of <AOC, then ... m<AOB+ m< BOC =…

Postulate 1: Ruler Postulate

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

Postulate 2: 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 noncollinear points, there is exactly one pl…

A line contains at least two points

A plane contains at least three noncollinear points

Postulate 2.1

Through any two points, there is exactly one line

Postulate 2.2

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

Postulate 1.1

Postulate 1.2

Postulate 1.3

Postulate 1.4

Through any 2 points there is exactly one line.

If two lines intersect then they intersect at exactly one poin…

If two planes intersect then they intersect at exactly one lin…

Through any 3 Non-Collinear points there is exactly one plane.

Postulate 1.1

Through any 2 points there is exactly one line.

Postulate 1.2

If two lines intersect then they intersect at exactly one poin…

4.1

4.2

4.3

4.4

the acute angles of a right triangle are complementary

there can be at most one right or obtuse angle in a triangle

a triangle is equilateral if and only if it is equiangular

each angle of an equilateral triangle measures 60 degrees

4.1

the acute angles of a right triangle are complementary

4.2

there can be at most one right or obtuse angle in a triangle

Theorem 5.3 (Circumcenter Theorem)

Theorem 5.4 (Angle Bisector Theorem)

Theorem 5.5 (Converse of the Angle Bise…

Theorem 5.6 (Incenter Theorem)

The perpendicular bisectors of a triangle intersect at a point…

If a point is on the bisectors of an angle, then it is equidis…

If a point in the interior of an angle is equidistant from the…

The angle bisectors of a triangle intersect at a point called…

Theorem 5.3 (Circumcenter Theorem)

The perpendicular bisectors of a triangle intersect at a point…

Theorem 5.4 (Angle Bisector Theorem)

If a point is on the bisectors of an angle, then it is equidis…

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

Through any two points there is exactly one line

Through any three nonlinear points there is exactly one plane…

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

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

Postulate 1-1-1

Through any two points there is exactly one line

Postulate 1-1-2

Through any three nonlinear points there is exactly one plane…

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

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

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

If two sides and the included side of one triangle are congrue…

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

Side-Side-Side (SSS)

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

Side-Angle-Side (SAS)

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

Ruler Postulate #1

Segment Addition Postulate #2

Protractor Postulate #3

Angle Addition Postulate #4

Ruler Postulate #1... the points on a line can be matched one to…

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

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

if p is in the interior of RST then mRSP+mPSt = mRST

Ruler Postulate #1

Ruler Postulate #1... the points on a line can be matched one to…

Segment Addition Postulate #2

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

Reflexive property of equality

Symmetric property of equality

Transitive property of equality

Substitution property of equality

Anything that is equal to itself (a=a) ; Reflect=mirror

Flip things around with a equals sign (2x=a)

Train effect, if a=b and b=c then a=c

Allows you to substitute with an equivalent value (7+15+2x, 22…

Reflexive property of equality

Anything that is equal to itself (a=a) ; Reflect=mirror

Symmetric property of equality

Flip things around with a equals sign (2x=a)

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

through any two points there is exactly one line

through any three noncollinear points there is exactly one pla…

if two points lie in a plane, then the line containing these p…

if two lines intersect, then they intersect in exactly one poi…

Postulate 1-1-1

through any two points there is exactly one line

Postulate 1-1-2

through any three noncollinear points there is exactly one pla…

Segment Addition Postulate

Angle Addition Postulate

Point, Line, Plane Postulate 1

Point, Line, Plane Postulate 2

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

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

Through any two points there exists exactly one line.

A line contains at least two points.

Segment Addition Postulate

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

Angle Addition Postulate

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

Polygon Exterior Angle Corollary

Quadrilateral Exterior Angle Sum Coroll…

Quadrilateral Interior Angle Sum Coroll…

Regular Polygon Interior Angle Corollary

the measure of each exterior and of a regular polygon of n sid…

the sum of the four exterior angles of a quadrilateral is 360°

the sum of the four interior angles of a quadrilateral is 360°

the measure of each interior angle of a regular polygon of n s…

Polygon Exterior Angle Corollary

the measure of each exterior and of a regular polygon of n sid…

Quadrilateral Exterior Angle Sum Coroll…

the sum of the four exterior angles of a quadrilateral is 360°

Segment Addition Postulate

Angle Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

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

If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR

In a right triangle, the sum of the squares if the lengths of…

If two angles form a linear pair then they are supplementary

Segment Addition Postulate

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

Angle Addition Postulate

If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR

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 pairs…

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

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 pairs…

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 tw…

all right angles are congruent

if two angles are complementary to the same angle, then the tw…

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 tw…

if two angles of a triangle are congrue…

each angle of an equiangular

in a triangle there is at most

acute angles of a right triangle

another triangle the third angles are congruent

triangle has a measure of 60 degrees

one right angle or one obtuse angle

are complementary

if two angles of a triangle are congrue…

another triangle the third angles are congruent

each angle of an equiangular

triangle has a measure of 60 degrees