# Study sets matching "postulates geometry theorems laws"

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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…

law of detachment (LOD)

law of syllogism (LOS)

contrapositive of a true statement is t…

reflexive

you can take part of an "if then" statement out if you know th…

if two parts of a statement are set equal to the same third st…

if a statement is true, then its contrapositive is also true

any measure or shape is equal to or congruent to itself

law of detachment (LOD)

you can take part of an "if then" statement out if you know th…

law of syllogism (LOS)

if two parts of a statement are set equal to the same third st…

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…

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…

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°

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.

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 2 points there can only be one line

if 2 lines intersect, then they intersect at exactly 1 point

if 2 planes intersect, then they intersect in exactly 1 line

through any 3 non-collinear points there is exactly 1 plane

postulate 1-1

through any 2 points there can only be one line

postulate 1-2

if 2 lines intersect, then they intersect at exactly 1 point

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°

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

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

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 a…

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

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 th…

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

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 th…

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement (if-then statement), the statement…

A statement written in an if then form... A statement of the form…

An educated guess based on known information... pg 78

The statement formed by negating both the hypothesis(educated…

Conclusion

In a conditional statement (if-then statement), the statement…

Conditional Statement

A statement written in an if then form... A statement of the form…

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

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

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 ang…

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

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

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

Corresponding Angles Converse

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

Alternate Interior Angles Converse

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

Transitive Property of Equality

Symmetric Property of Equality

Reflexive Property of Equality

Substitution Property of Equality

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

If a=b then b=a

For any real number a, a=a

If a=b, then a can be substituted for b in any equation for ex…

Transitive Property of Equality

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

Symmetric Property of Equality

If a=b then b=a

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 syllogism

law of detachment

reflexive property of equality

symmetric property of equality

if P --> Q and Q --> r is true, then p --> R is a true stateme…

if P --> Q is true and P is true, then Q is true

a=a

if a=b, then b=a

law of syllogism

if P --> Q and Q --> r is true, then p --> R is a true stateme…

law of detachment

if P --> Q is true and P is true, then Q is true

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…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Ruler Postulate

If a=a, then a=a

If a=b, then b=a

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

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

Reflexive Property of Equality

If a=a, then a=a

Symmetric Property of Equality

If a=b, then b=a

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

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