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

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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

Always - Sometimes - Never: Two planes…

Always - Sometimes - Never: Perpendicul…

Always-Sometimes-Never: Two noncollinea…

If b - 7 = 7, then b = 14.

Sometimes - 2 planes don't always intersect

Always - perpendicular lines intersect and form right angles

Never - 3 noncollinear points form a plane

Addition Propertry of Equality

Always - Sometimes - Never: Two planes…

Sometimes - 2 planes don't always intersect

Always - Sometimes - Never: Perpendicul…

Always - perpendicular lines intersect and form right angles

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 and c ≠ 0, then a÷c = b÷c

addition property

subtraction property

multiplication property

division property

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

addition property

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

subtraction property

Definition of congruent segments

Definition of congruent angles

Definition of segment bisector

Definition of angle bisector

two segments that are equal

two angles that have equal measure

intersects at the midpoint

ray that divides two adjacent angles into two congruent angles

Definition of congruent segments

two segments that are equal

Definition of congruent angles

two angles that have equal measure

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 of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

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=bc

if a=b and c≠0, then c÷a=c÷b

Addition Property of Equality

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

Subtraction Property of Equality

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

Transitive property of equality/ congru…

Reflexive property of equality/ congrue…

symmetric property of equality/ congrue…

addition property of equality

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

a=a

if a=b then b=a

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

Transitive property of equality/ congru…

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

Reflexive property of equality/ congrue…

a=a

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 + c = b + c.

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b, then b = a.

Segment Addition Postulate

Angle Addition Postulate

Two Point Postulate

Right Angles

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 the measure of <RST is e…

Through any two points, there exists exactly one line.

If angles are right, then they are congruent.... <CBA and <DBA ar…

Segment Addition Postulate

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

Angle Addition Postulate

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

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…

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

If a = b, c not equal to "zero", 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

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

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 Theorem

Right Angle Congruence Theorem

Linear Pair Postulate

Theorem

Vertical angles are equal in measure

All right angles are congruent

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

If two congruent angles are supplementary, then each is a righ…

Vertical Angles Theorem

Vertical angles are equal in measure

Right Angle Congruence Theorem

All right angles are congruent

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 and c ≠ 0, then a÷c = b÷c

addition property

subtraction property

multiplication property

division property

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

addition property

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

subtraction property

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any 2 points there is exactly one 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 there is exactly one line.

Postulate 2.2

Through any 3 noncollinear points there is exactly one plane.

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

Transitive Property

Supplement Theorem

Congruent Supplements Theorem

Right Angle Theorums

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

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

If 2 angles are supplementary to the same angle, then the 2 an…

Perpendicular lines form right angles... All right angles are con…

Transitive Property

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

Supplement Theorem

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

Definition of Opposite Rays

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Two rays that have a common endpoint and form a line

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

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 d…

Definition of Opposite Rays

Two rays that have a common endpoint and form a line

Ruler Postulate

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

Segment Addition Postulate

Definition of Midpoint

Definition of a Segment Bisector

Angle Addition Postulate

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

A point that divides a segment into two congruent segments

A point, ray, line, or line segment, or plane that intersects…

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

Segment Addition Postulate

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

Definition of Midpoint

A point that divides a segment into two congruent segments

Segment Addition Postulate

Midpoint of a Segment

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=m<AOC

Segment Addition Postulate

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

Midpoint of a Segment

The point that divides the segment into two congruent segments

If two lines intersect,..

Through a line and a point not in the l…

If two lines intersect,...

Midpoint Theorem

then they intersect in EXACTLY one point

there is EXACTLY one plane

then EXACTLY one plane contains the lines

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

If two lines intersect,..

then they intersect in EXACTLY one point

Through a line and a point not in the l…

there is EXACTLY one plane

Def of collinear

Def of coplanar

Point, lines, and planes

Segment Add Postulate

Points that are on the same line

Points and other figures that lie in the same plane

The 3 undefined terms of Geometry

If point Y is between points X and Z, then XY + YZ =XZ

Def of collinear

Points that are on the same line

Def of coplanar

Points and other figures that lie in the same plane