# Study sets matching "geometry theorems and definitions postulates properties"

Ruler Postulate

Segment Addition Postulate

Definition of a midpoint of a segment

Definition of a bisector of a segment

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

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

The point that divides the segment into two congruent segments…

The line, segment, ray, or plane that intersects the segment a…

Ruler Postulate

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

Segment Addition Postulate

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

Segment Addition Postulate

Angle Addition Postulate

Conditional Definition

Definition of Linear Pair

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

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

If p then q

When the non shared sides of two adjacent angles form opposite…

Segment Addition Postulate

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

Angle Addition Postulate

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

Complementary Angles

Supplementary Angles

Vertical Angles

Transversal

Angles that add up to 90 degrees

Angles that add up to 180 degrees

Two angles across from each other when lines intersect

A line that intersects two parallel lines

Complementary Angles

Angles that add up to 90 degrees

Supplementary Angles

Angles that add up to 180 degrees

Identity Properties

Commutative Properties

Associative Properties

Inverse Properties

Addition- a+0=a and 0+a=a... Multiplication- a

**1=a 1**a=aAddition- a+b=b+a... Multiplication- a

**b=b**aAddition- (a+b)+c=a+(b+c)... Multiplication- (a

**b)**c=a**(b**c)Addition- the sum of another number and its opposite, or addit…

Identity Properties

Addition- a+0=a and 0+a=a... Multiplication- a

**1=a 1**a=aCommutative Properties

Addition- a+b=b+a... Multiplication- a

**b=b**aAddition Property

Subtraction Property

Multiplication Property

Division Property

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

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

If a=b, a

**c = a**bIf a=b and c≠0, then a/c = b/c

Addition Property

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

Subtraction Property

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

Segment Addition Postulate

Angle Addition Postulate

Conditional Definition

Definition of Linear Pair

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

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

If p then q

When the non shared sides of two adjacent angles form opposite…

Segment Addition Postulate

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

Angle Addition Postulate

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

One line

One plane

By its three noncollinear points or by…

A line

Through any teo points there is exactly...

Through any three noncollinear points, there is exactly...

Name a plane

Contains at least two points

One line

Through any teo points there is exactly...

One plane

Through any three noncollinear points, there is exactly...

Addition Property of Equality (POE)

Subtraction Property of Equality (POE)

Multiplication Property of Equality (PO…

Division Property of Equality (POE)

If a = b and c =d, ... then a + c = b + d

If a = b and c = d, ... then a - c = b - d

If a = b, ... then ac = cb

If a = b and c ≠ 0, ... then a/c = b/c

Addition Property of Equality (POE)

If a = b and c =d, ... then a + c = b + d

Subtraction Property of Equality (POE)

If a = b and c = d, ... then a - c = b - d

Vertical Angles Congruence Theorem

Congruent supplements theorem

Congruent compliments theorem

Right Angle Congruence Theorem

Vertical angles are congruent

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

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

All right angles are congruent

Vertical Angles Congruence Theorem

Vertical angles are congruent

Congruent supplements theorem

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

Segment Addition Postulate

Angle Addition Postulate (Pt. 1)

Angle Addition Postulate (Pt. 2)

Midpoint Theorem

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

If B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC

If ∠AOC = 180° and B is any point not on ↔AC, then m∠AOC + m∠B…

If M is the midpoint of line segment AB, then AM= 1/2 AB and M…

Segment Addition Postulate

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

Angle Addition Postulate (Pt. 1)

If B is in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC

Def RT

Def perpendicular

Law of detachment

Law of contrapositive

Right angles are 90 degrees

a straight line at an angle of 90

If p->q then Q must be true

If p ->q then ~Q -> ~P must be true

Def RT

Right angles are 90 degrees

Def perpendicular

a straight line at an angle of 90

Unit 1

Postulate 1.1

Postulate 1.2

Postulate 1.3

...

Any two points make up one line.

Two lines can only intersect at one point.

Two planes can only intersect through one line.

Unit 1

...

Postulate 1.1

Any two points make up one line.

definition of perpendicular lines

addition property

subtraction property

multiplication property

if 2 lines intersect to form a right angle, then they are perp…

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

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

if a = b, then ac = bc

definition of perpendicular lines

if 2 lines intersect to form a right angle, then they are perp…

addition property

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

Addition property

Subtraction property

Multiplication property

Division property

a=b and c=d, then a+c = b+d

a=b and c=d, then a-c = b-d

a=b, then ca = cb

a=b, then a/c = b/c where C doesn't = 0

Addition property

a=b and c=d, then a+c = b+d

Subtraction property

a=b and c=d, then a-c = b-d

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 and c is not equal to 0 then a/c=b/c

Addition Property of Equality

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

Subtraction Property of Equality

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

Definition 1

Definition 2

Postulate 1

Postulate 2

Collinear Points are points are points that lie on the same li…

Noncollinear points are points that do not lie on the same lin…

Two points determine a unique straight line.

Three noncollinear points determine a unique plane.

Definition 1

Collinear Points are points are points that lie on the same li…

Definition 2

Noncollinear points are points that do not lie on the same lin…

Reflexive Property

Substitution Property

Transitive

Theorem 2-1

a = a

If a = b, then either a or b may be substituted for the other…

If a = b and b = c, then a = c

If M is the midpoint of AB, then AM = 1/2AB and MB = 1/2AB

Reflexive Property

a = a

Substitution Property

If a = b, then either a or b may be substituted for the other…

Vertical angles

Angle bisector

Segment bisector

Midpoint

Two angles whose sides form two pairs of opposite rays

A ray that divides an angle into two adjacent angles that are…

A segment, Ray, line, or plane that intersects a segment at it…

The point that divides, or bisects a segment into 2 congruent…

Vertical angles

Two angles whose sides form two pairs of opposite rays

Angle bisector

A ray that divides an angle into two adjacent angles that are…

Definition of congruence

Segment Addition Postulate

Transitive property

Symmetric property of Equality

If AB=CD then line segment AB is congruent to line segment CD

AB+BC=AC

if AB=CD and CD=EF then AB=EF

if AB=CD then CD=AB

Definition of congruence

If AB=CD then line segment AB is congruent to line segment CD

Segment Addition Postulate

AB+BC=AC

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

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

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

If a=b, then ac=bc

If a=b, then a/c=b/c

Addition Property of Equality

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

Subtraction Property of Equality

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

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 and c =/, then a/c = b/c

Addition Property of Equality

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

Subtraction Property of Equality

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

Addition Property

Subtraction Property

Multiplication Property

Division Property

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 and c ≠ 0, then a/c = b/c.

Addition Property

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

Subtraction Property

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

Collinear Points

Noncollinear Points

Line Postulate

Plane Postulate

Points that lie on the same line.

Points that do not lie on the same line.

Two points determine a unique straight line.

Three noncollinear points determine a unique plane.

Collinear Points

Points that lie on the same line.

Noncollinear Points

Points that do not lie on the same line.

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Property

Addition Property of Equality

If point B is between A and C on a line, then AB+BC=AC

If D is in the interior of <ABC then: m<ABD+m<DBC=m<ABC

If two <'s form a straight line, then they are supplementary

x-4=11 ... x=15

Segment Addition Postulate

If point B is between A and C on a line, then AB+BC=AC

Angle Addition Postulate

If D is in the interior of <ABC then: m<ABD+m<DBC=m<ABC

def. supplementary

def. supplementary

def. complementary

def. right angle

m<1+m<2=180... <1 supp <2

<A supp <B... m<A + m<B =180

<1 comp <2... m<1 + m<2=90

<ABC is a rt <... m<ABC=90

def. supplementary

m<1+m<2=180... <1 supp <2

def. supplementary

<A supp <B... m<A + m<B =180