# Study sets matching "postulates"

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Short Title for the 5 Ways

What does each proof conclude?

Proof from motion to the necessity of a…

Proof from motion to the necessity of a…

Proof from motion; Proof from Efficient Causes; Proof from the…

Each postulates the necessity of a unique existence very diffe…

Moved; things change around us constantly.

Everything that is moved is moved by ??????

Short Title for the 5 Ways

Proof from motion; Proof from Efficient Causes; Proof from the…

What does each proof conclude?

Each postulates the necessity of a unique existence very diffe…

Inductive Reasoning

Conjecture

Deductive Reasoning

If-Then Conditional

Using specific examples to make a general conclusion

A guess

Applying rules to specific situations to form a conclusion

p => q

Inductive Reasoning

Using specific examples to make a general conclusion

Conjecture

A guess

Reflexive Property

Transitive Property

Addition Postulate

Subtraction Postulate

A quantity is congruent (equal) to itself. a = a

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

Where you add on both sides

Where you subtract on both sides

Reflexive Property

A quantity is congruent (equal) to itself. a = a

Transitive Property

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

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Postulate

Vertical Angles Theorem

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

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

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

If two angles are vertical angles, then they are congruent.

Segment Addition Postulate

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

Angle Addition Postulate

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

Definition of Supplementary

Definition of Complementary

Definition of Right angle

Definition of Midpoint

Angles that add up to 180 degree

Angles that add up to 90 degree

An angle that is 90 degree

The midpoint is the middle point of a line segment

Definition of Supplementary

Angles that add up to 180 degree

Definition of Complementary

Angles that add up to 90 degree

Converse

Inverse

Contrapositive

Reflexive

Switch the hypothesis and the conclusion. q-p, if q then p

negate both the hypothesis and the conclusion of the condition…

Negate both the hypothesis and the conclusion of the converse,…

a=a

Converse

Switch the hypothesis and the conclusion. q-p, if q then p

Inverse

negate both the hypothesis and the conclusion of the condition…

postulate 5

postulate 6

postulate 7

postulate 8

through any 2 points there exists only 1 line

a line contains at least 2 points

if 2 lines intersect, then their intersection is exactly 1 poi…

through any 3 noncollinear points there exists exactly one pla…

postulate 5

through any 2 points there exists only 1 line

postulate 6

a line contains at least 2 points

Betweenness of points

Definition of midpoint

Definition of congruent segments

Definition of congruent angles

G: M is between P and Q... S: PM+MQ=PQ

____... G: M is the midpoint of PQ... R: PM=MQ

___ ~ ___... G: AB = CD ... R: AB=CD

G: ∠ABC≅ ∠DEF... R: m∠ABC=m∠DEF

Betweenness of points

G: M is between P and Q... S: PM+MQ=PQ

Definition of midpoint

____... G: M is the midpoint of PQ... R: PM=MQ

point

Line

Line segment

Ray

has 0 dimension and is on a line they are usually labeled

contains and infinite number of points

is a part of a line and it consists of two end points and all…

has a well defined starting point and keep going on, on the ot…

point

has 0 dimension and is on a line they are usually labeled

Line

contains and infinite number of points

Point

Line

Plane

Postulates

A specific place in space

A set of continuous points that extend indefinitley

Flat surface that extends indefinitley in all directions

Generalizations that cannot be proven true... 1. 2 points determ…

Point

A specific place in space

Line

A set of continuous points that extend indefinitley

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If you add the same number to each side of an equation, the tw…

If you subtract the same number from each side of an equation,…

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 you add the same number to each side of an equation, the tw…

Subtraction Property of Equality

If you subtract the same number from each side of an equation,…

Midpoint Theorem

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

If M is the midpoint of AB then AM is congruent ti MB.

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

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

If a=b, then a

**c=b**cMidpoint Theorem

If M is the midpoint of AB then AM is congruent ti MB.

Addition Property of Equality

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

Side-Side-Side Similarity (SSS ~)

Side-Angle-Side Similarity (SAS ~)

Angle-Angle Similarity (AA ~)

Corresponding Angles In Parallel Lines

Where 3 sides of one triangle are proportional to 3 correspond…

Where 2 sides of one triangle are proportional to 2 correspond…

Where 2 angles of one triangle are congruent to 2 angles of an…

Are Congruent

Side-Side-Side Similarity (SSS ~)

Where 3 sides of one triangle are proportional to 3 correspond…

Side-Angle-Side Similarity (SAS ~)

Where 2 sides of one triangle are proportional to 2 correspond…

Side-Side-Side Similarity (SSS ~)

Side-Angle-Side Similarity (SAS ~)

Angle-Angle Similarity (AA ~)

Corresponding Angles In Parallel Lines

Where 3 sides of one triangle are proportional to 3 correspond…

Where 2 sides of one triangle are proportional to 2 correspond…

Where 2 angles of one triangle are congruent to 2 angles of an…

Are Congruent

Side-Side-Side Similarity (SSS ~)

Where 3 sides of one triangle are proportional to 3 correspond…

Side-Angle-Side Similarity (SAS ~)

Where 2 sides of one triangle are proportional to 2 correspond…

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

Two Point Postulate

Line-Point Postulate

Line Intersection Postulate

Three Point Postulate

through any two points, there exists exactly one line

a line contains at least two points

if two lines intersect, then their intersection is exactly one…

through any three noncollinear points, there exists exactly on…

Two Point Postulate

through any two points, there exists exactly one line

Line-Point Postulate

a line contains at least two points

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

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