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

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

Definition of Midpoint

Definition of Bisector

Definition of Angle Bisector

Definition of Perpendicular

The point halfway between two given points.

A line segment, line, or plane that divides a geometric figur…

A line or ray that divides an angle in half.

Two lines bisect and form a 90 degree angle.

Definition of Midpoint

The point halfway between two given points.

Definition of Bisector

A line segment, line, or plane that divides a geometric figur…

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 s…

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

The point that divides the segment into two congruent segment…

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

Ruler Postulate

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

Segment Addition Postulate

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

Definition of congruent segments

Definition of congruent angles

Definition of right angle

Definition of linear pair

1. If segments are congruent, then they have the same measure…

1. If angles are congruent, then they have the same measure.…

1. If an angle has a measure of 90 degrees, then it is a righ…

1. If angles are adjacent angles and are formed by opposite r…

Definition of congruent segments

1. If segments are congruent, then they have the same measure…

Definition of congruent angles

1. If angles are congruent, then they have the same measure.…

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…

If p then q

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

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…

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

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…

If p then q

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

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…

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...

Reflexive Property

Transitive Property

Subtraction Property

Congruent Supplements Theorem

Any quantity is equal/congruent to itself.

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

If a=b and c=d, then a-c=b-d. When equal quantities are subtr…

If two angles are supplements of the same angle (or of congru…

Reflexive Property

Any quantity is equal/congruent to itself.

Transitive Property

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

Addition Property of Equality (POE)

Subtraction Property of Equality (POE)

Multiplication Property of Equality (P…

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

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

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.

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

If you take a line segment and divide it into equal segments…

If B is between A and C, then AB + BC = AC (the parts add up…

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

If point B lies in the interior of /_AOC, then the m/_AOB + m…

Ruler Postulate

If you take a line segment and divide it into equal segments…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC (the parts add up…

definition of perpendicular lines

addition property

subtraction property

multiplication property

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

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 per…

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

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∠…

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

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

Perpendicular Transversal Theorem

Segment Addition Postulate

CPCTC

Third Angle Theorem

In a plane, if a line, or transversal, is perpendicular to on…

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

Corresponding parts of congruent triangles are congruent

If two angles of one triangle are congruent to two angles of…

Perpendicular Transversal Theorem

In a plane, if a line, or transversal, is perpendicular to on…

Segment Addition Postulate

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

Definition 1

Definition 2

Postulate 1

Postulate 2

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

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

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 l…

Definition 2

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

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

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 i…

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…

Angle Addition Postulate

Corresponding Angles Postulate

Parallel Postulate

Coplanar

If a point lies on the interior of an angle, that angle is th…

If a transversal intersects two parallel lines, the pairs of…

Given a line and a point not on that line, there exists a uni…

Two lines that are on the same plane

Angle Addition Postulate

If a point lies on the interior of an angle, that angle is th…

Corresponding Angles Postulate

If a transversal intersects two parallel lines, the pairs of…

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.

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 x c=b x c

If a=b, then a/b=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

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 addi…

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**aPerpendicular Transversal Theorem

Segment Addition Postulate

CPCTC

Third Angle Theorem

In a plane, if a line, or transversal, is perpendicular to on…

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

Corresponding parts of congruent triangles are congruent

If two angles of one triangle are congruent to two angles of…

Perpendicular Transversal Theorem

In a plane, if a line, or transversal, is perpendicular to on…

Segment Addition Postulate

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

Perpendicular Transversal Theorem

Segment Addition Postulate

CPCTC

Third Angle Theorem

In a plane, if a line, or transversal, is perpendicular to on…

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

Corresponding parts of congruent triangles are congruent

If two angles of one triangle are congruent to two angles of…

Perpendicular Transversal Theorem

In a plane, if a line, or transversal, is perpendicular to on…

Segment Addition Postulate

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

If S isn in the interior of ∠PQR... Then…

If JK (ray) bisects ∠LJM... Then ∠LJK≅ ∠KJM

If ∠APC = ∠BPC... Then AC = BC

If two angle measures have a sum of 90…

Angle addition postulate

Definition of angle bisector

Angle bisector theorem

Definition of complimentary angles

If S isn in the interior of ∠PQR... Then…

Angle addition postulate

If JK (ray) bisects ∠LJM... Then ∠LJK≅ ∠KJM

Definition of angle bisector

Midpoint of a segment

Bisector of an angle

Complementary angles

Supplementary angles

the point that divides the segment into two congruent segments

line, ray, or segment that divides the angle into two congrue…

two angles whose sum is 90 degrees

two angles whose sum is 180 degrees

Midpoint of a segment

the point that divides the segment into two congruent segments

Bisector of an angle

line, ray, or segment that divides the angle into two congrue…

Segment Addition Postualtes

Angle Addition Postulate

Linear Pair Theorem

Congruent Complements Theorem

If B is between A and C, the AB+BC=AC (part + part = whole)

If C is in the interior of ∠AOD, then m∠AOC + m∠COD = m∠AOD (…

if 2 ∠'s form a linear pair, then they are supplementary (180°)

If 2 ∠'s are complementary (90°) to the same ∠ or to ≅ ∠'s th…

Segment Addition Postualtes

If B is between A and C, the AB+BC=AC (part + part = whole)

Angle Addition Postulate

If C is in the interior of ∠AOD, then m∠AOC + m∠COD = m∠AOD (…

Definition of congruent segments

Definition of congruent angles

Definition of right angle

Definition of linear pair

1. If segments are congruent, then they have the same measure…

1. If angles are congruent, then they have the same measure.…

1. If an angle has a measure of 90 degrees, then it is a righ…

1. If angles are adjacent angles and are formed by opposite r…

Definition of congruent segments

1. If segments are congruent, then they have the same measure…

Definition of congruent angles

1. If angles are congruent, then they have the same measure.…

Definition of congruent segs/∠s

Definition of right angle

Definition of perpendicular

Definition of bisect

1. If segs/∠s are ≅, then segs/∠s have the same measure.... 2. I…

1. If ∠ is 90°, then ∠ is a rt. ∠.... 2. If ∠ is a rt. ∠, then ∠…

1. If lines form rt. ∠s, then they are ⊥.... 2. If lines are ⊥,…

1. If seg/∠ is bisected, then seg/∠ is div. into two ≅ parts.…

Definition of congruent segs/∠s

1. If segs/∠s are ≅, then segs/∠s have the same measure.... 2. I…

Definition of right angle

1. If ∠ is 90°, then ∠ is a rt. ∠.... 2. If ∠ is a rt. ∠, then ∠…

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.

The measure of ∠AOB, which can be written as m∠AOB, is equal…

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

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.

definition of congruent segments

definition of congruent angles

definition of right angles

definition of midpoint

Angle ABC is a right angle... The measure of angle ABC = 90 degr…

definition of congruent segments

definition of congruent angles

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…

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

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

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

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

Segment Addition Postulate

Angle Addition Postulate

Definition of a Midpoint

Definition of a Right Angle

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

If S is inside of PQR then PQS + SQR = PQR

If the point is a midpoint then it bisects a segment (Two con…

If an angle is a right angle then the angle's measure is 90 d…

Segment Addition Postulate

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

Angle Addition Postulate

If S is inside of PQR then PQS + SQR = PQR

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 ≠ 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.

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 and c≠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

Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

Protractor Postulate

Every point on a line can be paired with a real number. This…

If three points A, B, and c are collinear and B in between A…

If point B is in the interior of angle AOC, then the measurem…

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

Ruler Postulate

Every point on a line can be paired with a real number. This…

Segment Addition Postulate

If three points A, B, and c are collinear and B in between A…

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

definition of congruent segments

definition of congruent angles

definition of right angles

definition of midpoint

Angle ABC is a right angle... The measure of angle ABC = 90 degr…

definition of congruent segments

definition of congruent angles

definition of congruent segments

definition of congruent angles

definition of right angles

definition of midpoint

Angle ABC is a right angle... The measure of angle ABC = 90 degr…

definition of congruent segments

definition of congruent angles

Addtition Property

Subtraction Property

Multiplication Property

Division Property

You can add the same # to both sides of an equation

You can subtract the same # from both sides of an equation

You can multiply two sides of an equation by the same thing

You can divide both sides of an equation by the same thing

Addtition Property

You can add the same # to both sides of an equation

Subtraction Property

You can subtract the same # from both sides of an equation

midpoint

segment bisector

congruent segments

angle bisector

the point halfway between the endpoints of a segment

any segment, line, or plane that intersects a segment at its…

segments that have the same measure

a ray that divides an angle into two congruent angles

midpoint

the point halfway between the endpoints of a segment

segment bisector

any segment, line, or plane that intersects a segment at its…