#### Study sets matching "postulates geometry theorems laws"

#### Study sets matching "postulates geometry theorems laws"

Law of Detatchment

Law of Syllogism

Postulate 1.1

Postulate 1.2

If p --> q is a true statement, and p is true, then q is true.

If p --> q, and q --> r, then p --> r.

Through any 2 points there exists exactly one line

If 2 distinct lines intersect, then they intersect in exactly…

Law of Detatchment

If p --> q is a true statement, and p is true, then q is true.

Law of Syllogism

If p --> q, and q --> r, then p --> r.

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line.

If two lines intersect, then they intersect in exactly one po…

If two planes intersect, then they intersect in exactly one l…

Through any three noncollinear points there is exactly one pl…

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

If two lines intersect, then they intersect in exactly one po…

Law of Detatchment

Law of Syllogism

Postulate 1.1

Postulate 1.2

If p --> q is a true statement, and p is true, then q is true.

If p --> q, and q --> r, then p --> r.

Through any 2 points there exists exactly one line

If 2 distinct lines intersect, then they intersect in exactly…

Law of Detatchment

If p --> q is a true statement, and p is true, then q is true.

Law of Syllogism

If p --> q, and q --> r, then p --> r.

Segment addition postulate

Angle addition postulate

Linear pair postulate

Area addition postulate

If 3 pt. Are Collinear Ab+Bc=ac

Angle AOB+BOC=AOC

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

The area of a region is the su. Of the areas of its nonoverla…

Segment addition postulate

If 3 pt. Are Collinear Ab+Bc=ac

Angle addition postulate

Angle AOB+BOC=AOC

Ruler Postulate

Segment Addition Postulate

Distance Formula

Protractor Postulate

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

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

The distance between A(x₁,y₁) and B(x₂,y₂) =√(x₂-x₁)+(y₂-y₁)

If point O is the center of a circle and points A and B are o…

Ruler Postulate

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

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

distance of two points = absolute value of the difference of…

e.x.: if Y is between X and Z, then XY + YZ = XZ. ... If XY + YZ…

measure of an angle = absolute value of the difference of the…

e.x.: if D is in the interior of angle ABC, then the measure…

Ruler Postulate

distance of two points = absolute value of the difference of…

Segment Addition Postulate

e.x.: if Y is between X and Z, then XY + YZ = XZ. ... If XY + YZ…

Through any 2 points,

If 2 distinct lines intersect,

If 2 planes intersect,

Through any 3 non-collinear points,

there is exactly one line

then they intersect in exactly one point

then they intersect at exactly one line

there is exactly one plane

Through any 2 points,

there is exactly one line

If 2 distinct lines intersect,

then they intersect in exactly one point

Law of Detachment

Law of Syllogism

Segment Addition Postulate

Angle Addition Postulate

If p -> q is true and p is true, then q is true

If p -> q and q -> r, then p -> r

If points A, B, and C are collinear and B is between A and C,…

If point T is interior of ∠AXC, then m∠AXT + m∠TXC = m∠AXC

Law of Detachment

If p -> q is true and p is true, then q is true

Law of Syllogism

If p -> q and q -> r, then p -> r

All right angles are congruent

If <1 and <2 are supplementary and <3…

If <4 and <5 are complementary and <6…

vertical angles are congruent

right angles congruence theorem

Congruent Supplements Theorem

Congruent Complements Theorem

vertical angles congruence theorem

All right angles are congruent

right angles congruence theorem

If <1 and <2 are supplementary and <3…

Congruent Supplements Theorem

ruler postulate

segment addition postulate

angle addition postulate

law of syllogism

every point on a line can be paired with a real number

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

if point B is in the interior of angle AXC, then measure of a…

if p->q/q->p is true, then p->r is true, cancels out middle

ruler postulate

every point on a line can be paired with a real number

segment addition postulate

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

Complementary angles

Supplementary angles

Theorem

Vertical Angles

two angles whose measures have a sum of 90°

two angles who measures have a sum of 180°

a statement that can be proven

two angles formed by intersecting lines and facing in the opp…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

1-1

1-2

1-3

1-4

Through any two points there in exactly one line

Two distinct lines intersect in exactly one point

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

Through any non-collinear points, there is exactly one plane

1-1

Through any two points there in exactly one line

1-2

Two distinct lines intersect in exactly one point

1-1

1-2

1-3

1-4

Through any two points there in exactly one line

Two distinct lines intersect in exactly one point

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

Through any non-collinear points, there is exactly one plane

1-1

Through any two points there in exactly one line

1-2

Two distinct lines intersect in exactly one point

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

law of detachment

law of syllogism

postulate 5

postulate 6

if P implies Q is a true conditional statement and P is true,…

if P implies Q and Q implies R is true, then P implies R.

through any two points there exists exactly one line.

a line contains at least two points.

law of detachment

if P implies Q is a true conditional statement and P is true,…

law of syllogism

if P implies Q and Q implies R is true, then P implies R.

(2-4)Definition of midpoint:

(3-9)Definition of bisector:

(5-2)CPCF Theorem (segment):

(2-4)Definition of a circle:

If a point is the midpoint of a segment, it divides the segme…

If a figure is the the bisector of a segment, it divides the…

If figures are congruent, then corresponding segments are con…

If a figure is a circle, then its radii are congruent. (2-4)

(2-4)Definition of midpoint:

If a point is the midpoint of a segment, it divides the segme…

(3-9)Definition of bisector:

If a figure is the the bisector of a segment, it divides the…

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

any segment or angle is congruent/equal to itself (AB = AB) (…

have equal measure

If AB + BC = AC and AB=BC

segment addition postulate

AB + BC = AC

reflexive property

any segment or angle is congruent/equal to itself (AB = AB) (…

Law of detachment

Law of Syllogism

Reflexive Property

Symmetric Property

if p implies q is a true conditional statement and p is true…

if p implies q and q imply r are true conditional statements…

for any real number a, a=a

if a=b then b=a

Law of detachment

if p implies q is a true conditional statement and p is true…

Law of Syllogism

if p implies q and q imply r are true conditional statements…

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Segment Addition Postulate

Angle Addition Postulate

Definition of Midpoint & Bisector

Definition of Angle Bisector

If B is between A and C then the length of AC is equal to the…

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

A bisector bisects a line segment at its midpoint which divid…

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

Segment Addition Postulate

If B is between A and C then the length of AC is equal to the…

Angle Addition Postulate

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

Betweenness statement

Distance formula (on # line)

distance formula ( in coordinate plane)

Midpoint formula (on # line)

AB + CB = AB

D= absolute value of x2 minus x1 or absolute value of x1 minu…

D= the square root of (x2-x1)squared + (y2-y1)squared

M= x1+x2 over 2

Betweenness statement

AB + CB = AB

Distance formula (on # line)

D= absolute value of x2 minus x1 or absolute value of x1 minu…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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.

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

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

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.

corresponding angles

congruent corresponding angles

SSS Postulate

SAS Postulate

If two parallel lines are cut by a transversal, then correspo…

If two lines are cut by a transversal and corresponding angle…

If three sides of one triangle are congruent to three sides o…

If two sides and the included angle of one triangle are congr…

corresponding angles

If two parallel lines are cut by a transversal, then correspo…

congruent corresponding angles

If two lines are cut by a transversal and corresponding angle…

Postulate

Theorem

Intersection of 2 lines is exactly...

Intersection of 2 planes is exactly...

Statement accepted without proof

Conjecture (mathematical hypothesis) that has been proved

1 point

1 line

Postulate

Statement accepted without proof

Theorem

Conjecture (mathematical hypothesis) that has been proved

Law of Syllogism

Law of Detachment

Postulate 5

Postulate 6

If hypothesis p, then conclusion q.... If hypothesis q, then con…

If the hypothesis of a conditional statement is true, than th…

Through any two points there exists exactly one line.

A line consists of at least two points.

Law of Syllogism

If hypothesis p, then conclusion q.... If hypothesis q, then con…

Law of Detachment

If the hypothesis of a conditional statement is true, than th…

Perpendicular Bisector Theorem

Corresponding Angles Theorem

Alternate Interior Angles Theorem

Same-Side Interior Angles Postulate

If a point is on the perpendicular bisector of a segment, the…

If two parallel lines are cut by a transversal, then the pair…

If two parallels are cut by a transversal, then the pair of a…

If two parallel lines are cut by a transversal, then the pair…

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, the…

Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then the pair…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

1. The points on a line can be paired with the real numbers i…

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

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

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

Ruler Postulate

1. The points on a line can be paired with the real numbers i…

Segment Addition Postulate

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

segment addition postulate

law of detachment

conditional statement

hypothesis

if SRT are collinear and R is between S and T then SR + RT= ST

if the hypothesis of a conditional statement is true then the…

a statement in the form of if______then______

"if" portion of a conditional statement

segment addition postulate

if SRT are collinear and R is between S and T then SR + RT= ST

law of detachment

if the hypothesis of a conditional statement is true then the…

Unique Line Postulate

Intersecting Lines Postulate

Intersecting Planes Postulate

Plane Postulate

Through any two points there is exactly one line

If two lines intersect, then they intersect in exactly one po…

If two planes intersect, then they intersect in exactly one l…

Through any three nonlinear points there is exactly one plane

Unique Line Postulate

Through any two points there is exactly one line

Intersecting Lines Postulate

If two lines intersect, then they intersect in exactly one po…

Complementary angles

Supplementary angles

Theorem

Vertical Angles

two angles whose measures have a sum of 90°

two angles who measures have a sum of 180°

a statement that can be proven

two angles formed by intersecting lines and facing in the opp…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

Midpoint

Collinear

Straight Angles

Acute Angles

It is a midpoint if and only if it divides a segment into two…

3 or more points on the same line

The sides of a straight angle form a line

Acute angles are less than a right angle

Midpoint

It is a midpoint if and only if it divides a segment into two…

Collinear

3 or more points on the same line

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.

The distance between two points is the…

If A, B, and C are collinear and B is…

If B is on the interior of ∠ADC, then…

Any line segment will have exactly one…

ruler postulate

segment addition postulate

angle addition postulate

midpoint postulate

The distance between two points is the…

ruler postulate

If A, B, and C are collinear and B is…

segment addition postulate

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

If two parallel lines are cut by a transversal, then the pair…

If two parallel lines are cut by a transversal, then the pair…

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

The distance between two points is the…

If A, B, and C are collinear and B is…

If B is on the interior of ∠ADC, then…

Any line segment will have exactly one…

ruler postulate

segment addition postulate

angle addition postulate

midpoint postulate

The distance between two points is the…

ruler postulate

If A, B, and C are collinear and B is…

segment addition postulate

Corresponding Angles Converse

Alternate Interior Angles Converse

Alternative Exterior Angles Converse

Consecutive Interior Angles converse

If two lines are cut by a transversal so the corresponding an…

If two lines are cut by a transversal so the alternate interi…

if two lines are cut by a transversal so the alternate exteri…

If two lines are cut by a transversal so the consecutive inte…

Corresponding Angles Converse

If two lines are cut by a transversal so the corresponding an…

Alternate Interior Angles Converse

If two lines are cut by a transversal so the alternate interi…

Linear Pair Postulate

Law of Detachment (word definition)

Law of Detachment (symbolic form)

Law of Syllogism (symbolic form)

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

If the hypothesis of a true conditional is true, then the con…

If p --> q is true and p is true, then q is true.

If p --> q is true and q --> r is true, then p --> r is true.

Linear Pair Postulate

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

Law of Detachment (word definition)

If the hypothesis of a true conditional is true, then the con…

Theorems

Postulates

Triangle Congruency

Postulate 1

Something that is provable

Things you cannot mathematically prove but are nonetheless true

SSS, ASA, SAS, AAS, HL

(Ruler Postulate)... The points on a line can be paired with rea…

Theorems

Something that is provable

Postulates

Things you cannot mathematically prove but are nonetheless true

Segment addition postulate

Angle addition postulate

Postulate 5

Postulate 6

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

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

A line contains at least two points; a plane contains at leas…

Through any two points there is exactly one line.

Segment addition postulate

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

Angle addition postulate

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

Postulate - 2.1

Postulate - 2.2

Postulate - 2.3

Postulate - 2.4

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 non collinear points

Postulate - 2.1

Through any two points, there is exactly one line

Postulate - 2.2

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

Ruler Postulate

Segment Addition Postulate

Midpoint Formula

Distance Formula

Distance between points A and B (AB) is the absolute value of…

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

If A (x1,y1) and B(x2,y2) are points in a coordinate plane, t…

If A (x1,y1) and B (x2,y2) are points in a coordinate plane,…

Ruler Postulate

Distance between points A and B (AB) is the absolute value of…

Segment Addition Postulate

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

Postulates points, planes, and lines

Postulates- intersection of planes and…

Ruler Postulate

Segment Addition Postulate

1.) Through any two pointd there is exactly one line.... 2.) Thr…

4.) If two lines intersect, then they intersect at one point.…

Points on a line can b put to a one to one correspondence wit…

If a point is in between two points then the distance from fi…

Postulates points, planes, and lines

1.) Through any two pointd there is exactly one line.... 2.) Thr…

Postulates- intersection of planes and…

4.) If two lines intersect, then they intersect at one point.…

parallel lines

skew lines

parallel planes

transversal

Two lines that are coplanar and do NOT intersect.

Lines that do NOT intersect and are NOT coplanar.

Two planes that do NOT intersect.

A line that intersects two or more coplanar lines at differen…

parallel lines

Two lines that are coplanar and do NOT intersect.

skew lines

Lines that do NOT intersect and are NOT coplanar.

Corresponding Angles Postulate (3-1)

Alternate Interior Angles Theorem (3-1)

Consecutive Interior Angles Theorem (3…

Alternate Exterior Angles Theorem (3-3)

If two parallel lines are cut by a transversal, the correspon…

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

If two parallel lines are cut by a transversal, the consecuti…

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

Corresponding Angles Postulate (3-1)

If two parallel lines are cut by a transversal, the correspon…

Alternate Interior Angles Theorem (3-1)

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