#### Study sets matching "geometry postulates proofs"

#### Study sets matching "geometry postulates proofs"

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…

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

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

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…

Segment addition postulate 2

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

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 cong…

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

Vertical Angles Congruence Theorem

Vertical Angles are Congruent.

Linear Pair Postulate

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

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 of ray OB. The r…

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

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,…

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

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.

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 exact…

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

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

1-1

Through any two points there is exactly one line.

1-2

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

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

If two angles have the same measuremen…

If the angles are congruent two angles…

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

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 measuremen…

definition of congruent angles

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 a…

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

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

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

addition property of equality

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

subtraction property of equality

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

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, t…

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 the…

segment addition postulate (SAP)

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

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 p…

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 p…

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 p…

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 p…

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

Parallel Postulate

Segment Addition Postulate

Angle Addition Postulate

Segment Addition Postulate

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

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…

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 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.

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 opp…

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

points on a perpendicular bisector of a segment are equidista…

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

isosceles triangle thm

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

converse of the isosceles triangle thm

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

Postulate

Theorem

Postulate 2.1

Postulate 2.2

A statement that is accepted as true without proof.

Once a statement has been proven it is called a ________.

Through any two points, there is exactly one line.

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

Postulate

A statement that is accepted as true without proof.

Theorem

Once a statement has been proven it is called a ________.

Postulate 2.1 ... (Lines, points, planes)

Postulate 2.2 ... (Lines, points, planes)

Postulate 2.3... (Lines, points, planes)

Postulate 2.4 ... (Lines, points, planes)

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 noncollinear points

Postulate 2.1 ... (Lines, points, planes)

Through any two points, there is exactly one line.

Postulate 2.2 ... (Lines, points, planes)

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

Reflexive property of congruence

Symmetry property of congruence

Transitive property of congruence

Alternate interior angle theorem

when the variable equals itself

If a=b then b=a

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

if 2 parallel lines are intersected by a traversal, then alte…

Reflexive property of congruence

when the variable equals itself

Symmetry property of congruence

If a=b then b=a

Ruler Postulate(1)

Ruler Postulate(2)

Segment Addition Postulate

Protractor Postulate

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

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

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

Name the origin of a protractor, and create and to find a cer…

Ruler Postulate(1)

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

Ruler Postulate(2)

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

segment addition postulate

Def: Midpoint of a segment

Def: Bisector of a segment

angle addition postulate

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

The point that divides the segment into two congruent segments

A line, segment, ray, or plane that intersects the segment at…

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

segment addition postulate

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

Def: Midpoint of a segment

The point that divides the segment into two congruent segments

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be put into a one-to-one corresponde…

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

Given line AB and a point O on line AB, all rays that can be…

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

Ruler Postulate

The points on a line can be put into a one-to-one corresponde…

Segment Addition Postulate

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

Postulate or axion

Postulate 2.1

Postulate 2.2

Postulate 2.3

A statement that is accepted as true without proof

Through any two distinct points there exists only 1 line

Though any 2 distinct points there exists exactly 1 plane

A line contains at least 2 points

Postulate or axion

A statement that is accepted as true without proof

Postulate 2.1

Through any two distinct points there exists only 1 line

Ruler Postulate

Protractor Postulate

Angle Addition Postulate

Segment Addition Postulate

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

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

The angle addition postulate states that if B is in the inter…

If a point B lies on a line segment , then . That is, the dis…

Ruler Postulate

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

Protractor Postulate

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

Conditional Statement

Converse

Inverse

Contraposistive

A logical statement that has two parts; a hypothesis, and a c…

A conditional statement that switches the places of the hypot…

When the hypothesis and conclusion of a conditional statement…

When the hypothesis and conclusion of a conditional statement…

Conditional Statement

A logical statement that has two parts; a hypothesis, and a c…

Converse

A conditional statement that switches the places of the hypot…

Alternate Interior Angles Theorem

Same Side Interior Angles Theorem

Alternate Exterior Angles Theorem

Same Side Exterior Angles Theorem

If 2 parallel lines are intersected by a transversal, then al…

If 2 parallel lines are cut by a transversal, then same side…

If 2 parallel lines are cut by a transversal, the alternate e…

If 2 parallel lines are are cut by a transversal, the same si…

Alternate Interior Angles Theorem

If 2 parallel lines are intersected by a transversal, then al…

Same Side Interior Angles Theorem

If 2 parallel lines are cut by a transversal, then same side…

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

Corresponding Angle Postulate

Alternate Interior Angle Postulate

Alternate Exterior Angle Postulate

Same-Side Consecutive Interior Angles…

If 2 // lines are cut by a transversal then the corresponding…

If 2 // lines are cut by a transversal then all alternate int…

If 2 angles are cut by a transversal then all alternate exter…

If 2 parallel lines are cut by a transversal then same side i…

Corresponding Angle Postulate

If 2 // lines are cut by a transversal then the corresponding…

Alternate Interior Angle Postulate

If 2 // lines are cut by a transversal then all alternate int…

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Properties of a square

Properties of a rectangle

Properties of a rhombus

Properties of a parallelogram

Both pairs of opposite sides are congruent... Both pairs of oppo…

Both pairs of opposite sides parallel ... Both pairs of opposite…

Both pairs of opposite sides parallel... Both pairs of opposite…

A quadrilateral with both pairs of opposite sides congruent... B…

Properties of a square

Both pairs of opposite sides are congruent... Both pairs of oppo…

Properties of a rectangle

Both pairs of opposite sides parallel ... Both pairs of opposite…

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

Ruler Postulate

Segment Addition Postulate

Postulate

Protractor 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.

A rule accepted without proof

An angle can be measured from 0 to 180

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.

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

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Slopes of parallel lines

Parallel Postulate

Slopes of Perpendicular Lines

Symmetric Property

If 2 nonvertical lines are parallel then their slopes are equ…

Through a point not on a line, there is ONLY ONE parallel to…

If 2 nonvertical lines are perpendicular, then the product of…

If a=b then b=a

Slopes of parallel lines

If 2 nonvertical lines are parallel then their slopes are equ…

Parallel Postulate

Through a point not on a line, there is ONLY ONE parallel to…

Triangle Angle-Sum Theorem

Exterior angle Theorem

Triangle Angle Sum Corollaries

Definition of Congruent Polygons

The sum of the measures of the angles of a triangle is 180

The measure of an exterior angle of a triangle is equal to th…

The acute angles of a right triangle are complementary... There…

Two polygons are congruent if and only if their corresponding…

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180

Exterior angle Theorem

The measure of an exterior angle of a triangle is equal to th…

Conditional statements

Addition Property of Equality

Multiplication Property of Equality

Division Property of Equality

if-then statements with a hypothesis and a conclusion

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

If a = b, then ac = bc

If a = b, then a/c=b/c, if C≠0

Conditional statements

if-then statements with a hypothesis and a conclusion

Addition Property of Equality

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

Segment Addition Postulate (SAP)

VAT

Linear Pair Thm

AAP

AB + BC = AC

Two angles are vertical iff their sides form opposite rays

Two adjacent angles form a linear pair iff their non-common s…

Angle Addition Postulate states that if a point S lies in the…

Segment Addition Postulate (SAP)

AB + BC = AC

VAT

Two angles are vertical iff their sides form opposite rays

Post 1: Ruler Postulate

Post 4

Post 5

Post 6

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

Angle Addition Post

a line contains at least 3 points not all in one line; a spac…

Through any two points there is exactly one line

Post 1: Ruler Postulate

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

Post 4

Angle Addition Post

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, t…

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 the…

segment addition postulate (SAP)

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

angle addition postulate (AAP)

Angles can be added together if they are adjacent

Commutative

Associative

Identity

Inverse

Addition: a plus b equals b plus a... Mult: a times b equals b t…

Addition: a plus (b plus c) equals (a plus b) plus c... Mult: a…

Add: a plus 0 equals a... Mult: a times 1 equals a

Add: A plus negative a equals zero... Mult: a times 1/a equals 1

Commutative

Addition: a plus b equals b plus a... Mult: a times b equals b t…

Associative

Addition: a plus (b plus c) equals (a plus b) plus c... Mult: a…

segment addition postulate

reflexive property of congruence

symmetric property of congruence

Transitive property of congruence

if A,B, and C are collinear, then point B is between A and C…

segment AB is congruent to segment AB

if segment AB is congruent to segment CD, the segment CD is c…

if segment AB is congruent to segment CD and CD is congruent…

segment addition postulate

if A,B, and C are collinear, then point B is between A and C…

reflexive property of congruence

segment AB is congruent to segment AB

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

For every two points there is one line

Brought every three non collinear points there is one plane

For every line there are at least two points

Through every plain there are at least three points

Postulate 2.1

For every two points there is one line

Postulate 2.2

Brought every three non collinear points there is one plane