# Study sets matching "postulates geometry theorems laws"

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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 poi…

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

Through any three noncollinear points there is exactly one pla…

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 poi…

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.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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 o…

Ruler Postulate

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

Segment Addition Postulate

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

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

Postulate #1 Ruler Postulate

Postulate #2 Segment Addition Postulate

Distance Formula

Pythagorean Theorem

p. 17 The distance between points A and B, written as AB, is t…

p. 18 If B is between A and C, then AB plus BC equal AC. If AB…

p. 19 If A and B are points in a coordinate plane, then the di…

p. 20 Fundamental relation in Euclidean geometry among the thr…

Postulate #1 Ruler Postulate

p. 17 The distance between points A and B, written as AB, is t…

Postulate #2 Segment Addition Postulate

p. 18 If B is between A and C, then AB plus BC equal AC. If AB…

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 exact…

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

All right angles are congruent

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

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

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 a…

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 A…

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

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 A…

Symmetric Property

Reflexive property

Transitive property

Addition Property

AB=CD, then CD=AB

AB=AB

AB=CD and CD=EF, the AB=EF

Adding the same number to each side ... x-3=7... +3 +3

Symmetric Property

AB=CD, then CD=AB

Reflexive property

AB=AB

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 oppo…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

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 exact…

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 Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

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 Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

If two angles are supplementary to the same angle, then

they are congruent.... Right Angles Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

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 Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

If two angles are supplementary to the same angle, then

Linear Pairs are Supplementary.

Perpendicular Lines form right angles.

All right angles are congruent.

Supplements of congruent angles are con…

Right

Supplementary (Working with total of 4 angles)

Linear Pairs are Supplementary.

Perpendicular Lines form right angles.

they are congruent.... Right Angles Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

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 Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

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.

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…

Law of detachment

Law of Syllogism

Reflexive Property

Symmetric Property

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

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

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 t…

Law of Syllogism

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

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

The distance between two points is the…

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

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

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 b…

segment addition postulate

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 minus…

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 minus…

(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 segmen…

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

If figures are congruent, then corresponding segments are cong…

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 segmen…

(3-9)Definition of bisector:

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

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

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

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) (m…