# Study sets matching "geometry postulates proofs"

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Ruler Postulate 1

Segment addition postulate 2

Protractor Postulate 3

Postulate 5

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

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

ConsiderOB and a point A on one side of OB. The Rays of the fo…

Through any two points there exists exactly one line

Ruler Postulate 1

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

Segment addition postulate 2

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

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any 2 points is exactly 1 line.

Through any 3 noncollinear points, there is exactly one plane.

A line contains at least 2 points.

A plane contains at least 3 noncollinear points.

Postulate 2.1

Through any 2 points is exactly 1 line.

Postulate 2.2

Through any 3 noncollinear points, there is exactly one plane.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

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

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

Ruler Postulate

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

Segment Addition Postulate

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

deff of parellelogram

property of parellelogram

property of parellelogram

property of parellelogram

a quad with 2 sets of // sides

opp sides congruent

opp angles congruent

same side angles are supplementary

deff of parellelogram

a quad with 2 sets of // sides

property of parellelogram

opp sides congruent

2.1

2.2

2.3

2.4

through any 2 points, there is exactly 1 line

through any 3 noncollinear points, there is exactly 1 plane

a line contains at least 2 points

a plane contains at least 3 noncollinear points

2.1

through any 2 points, there is exactly 1 line

2.2

through any 3 noncollinear points, there is exactly 1 plane

Addition Property 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 ac=bc

if a=b, then a/c=b/c c is ALMOST equal to

Addition Property of Equality

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

Subtraction Property of Equality

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

Vertical Angles Congruence Theorem

Linear Pair Postulate

Congruent Supplements Theorem

Congruent Complements Theorem

Vertical Angles are Congruent.

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

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

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

Vertical Angles Congruence Theorem

Vertical Angles are Congruent.

Linear Pair Postulate

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

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

if a=b then a+c= b+c... you can add something to both sides of an…

if a=b then a-c= b-c... you can subtract something from both side…

if a=b then a x c = b x c... you can multiply both sides of an eq…

if a=b then a/c= b/c... you can divide both side of an equation b…

addition property of equality

if a=b then a+c= b+c... you can add something to both sides of an…

subtraction property of equality

if a=b then a-c= b-c... you can subtract something from both side…

segment addition postulate (SAP)

angle addition postulate (AAP)

addition property of equality

subtraction property of equality

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

Angles can be added together if they are adjacent

Adding a value to each side of an equation... if a=b, then a+c=b+c

subtracting a value from each side of an equation ... if a=b then…

segment addition postulate (SAP)

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

angle addition postulate (AAP)

Angles can be added together if they are adjacent

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…

Segment Addition postulate

Angle Addition postulate

Linear Pair postulate

Definition of Congruence

If M is between A and B, then AM+MB=AB.

If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.

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

If measures are equal, then parts are congruent.

Segment Addition postulate

If M is between A and B, then AM+MB=AB.

Angle Addition postulate

If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.

Ruler Postulate

Segment Addition Postulate

Protector Postulate

Angle Addition Postulate

AB = distance between endpoints

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

Ruler Postulate for Angles

Segment Addition Postulate for Angles

Ruler Postulate

AB = distance between endpoints

Segment Addition Postulate

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

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

If two angles have the same measurement…

If the angles are congruent two angles…

If a point, X, is in the interior of <A…

segment addition postulate

definition of congruent angles

definition of congruent angles

angle addition postulate

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

segment addition postulate

If two angles have the same measurement…

definition of congruent angles

1-1

1-2

1-3

1-4

Through any two points there is exactly one line.

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

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

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

1-1

Through any two points there is exactly one line.

1-2

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

2.1

2.2

2.3

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

2.1

Through any two points, there is exactly one line.

2.2

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

Parallel Postulate

Segment Addition Postulate

Angle Addition Postulate

Segment Addition Postulate

only one line can be drawn through a given point so that the l…

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

If R is in the interior of <PQS, then <PQR+<RQS=<PQS

Length of pieces of a segment sum to the total length

Parallel Postulate

only one line can be drawn through a given point so that the l…

Segment Addition Postulate

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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

isosceles triangle thm

converse of the isosceles triangle thm

perpendicular bisector thm

angle side angle post (asa)

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

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

points on a perpendicular bisector of a segment are equidistan…

if two angles and the included side of the triangle are congru…

isosceles triangle thm

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

converse of the isosceles triangle thm

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

given- <1 and <2 are a linear pair ... <1…

given- p is parallel to q... prove- <1= <2

given- 1=3... prove- p11q

Given- <1 and <2 are complementary... prov…

1. <1 and <2 are a linear pair... <1 ~= <2 (GIVEN)... 2. <1 and <2…

1. p is parallel to q (GIVEN)... 2. <1 = <3 (CAP)... 3. 2=3 (VERTICA…

1. 1=3 (GIVEN)... 2. 1=2 (ALTERNATE EXTERIOR)... 3. 2=3 (LOS)... 4.. (A…

1. given... 2. <1+<2= 90 (DEFINITION OF COMPLEMENTARY ANGLES)... 3.…

given- <1 and <2 are a linear pair ... <1…

1. <1 and <2 are a linear pair... <1 ~= <2 (GIVEN)... 2. <1 and <2…

given- p is parallel to q... prove- <1= <2

1. p is parallel to q (GIVEN)... 2. <1 = <3 (CAP)... 3. 2=3 (VERTICA…

Postulates (axioms)

Theorems

Reflexive

Symmetric

statement that seems to "obvious" that we accept them without…

a statement that is provided by deductive reasoning

a quantity is equal to itself

if equal quantities are equal to the same quantity then they a…

Postulates (axioms)

statement that seems to "obvious" that we accept them without…

Theorems

a statement that is provided by deductive reasoning

Reflexive

Symmetric

Transitive

Substitution

a quantity is equal to itself

an equality maybe expressed in either order

if equal quantities are equal to the same quantity then they a…

a quantity may be substituted for its equal

Reflexive

a quantity is equal to itself

Symmetric

an equality maybe expressed in either order

Proof

Postulate

Inductive reasoning

Conjecture

A logical argument that shows a statement to be true

A rule that is ... excepted without proof

And argument that goes from a specific statement to a general…

A unproven statement that is based on observation

Proof

A logical argument that shows a statement to be true

Postulate

A rule that is ... excepted without proof

2.1

2.2

2.3

2.4

through any 2 points, there is exactly one line

through any 3 non collinear points, there is exactly one plane

a line contains at least 2 points

a plane contains at least 3 non collinear points

2.1

through any 2 points, there is exactly one line

2.2

through any 3 non collinear points, there is exactly one plane