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Points

Through any two _______ there exists exactly one line.

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line

A _____ contains at least two points.

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exactly one

If two lines intersect, then their intersection is ______ _______ point.

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three

Through any _______ noncollinear points there exists exactly one plane.

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non collinear

A plane contains at least three ___________ points.

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plane

If two points lie in a plane, then the line containing them lies in the ________.

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planes

If two _________ intersect, then their intersection is a line.

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Addition Property

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

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Subtraction Property

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

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Multiplication Property

If a=b, then ac=bc.

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Division Property

If a=b and c≠0, then a/c=b/c.

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Substitution Property

If a=b, then a can be substituted for b in any equation or expression.

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Distributive Property

a(b+c)=ab+ac, where a, b, and c are real numbers.

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Reflexive Property

--Real Numbers--For any real number a, a=a.

--Segment Lengths--For any segment, line segment AB, AB=AB

--Angle Measure-- For any angle <A, m<A=m<A

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Symmetric Property

--Real Numbers-- For any real numbers a and b, if a=b, then b=a

--Segment Length-- For any segments _-AB-_ and _-CD-_, if AB=CD, then CD=AB

--Angle Measure-- For any angles <A and <B, if m<A=m<B, then m<B=m<A

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Transitive Property

--Real Numbers-- For any real numbers a, b, and c,if a=b and b=c, then a=c

--Segment Length-- For any segments _-AB-_, _-CD-_, and _-EF-_, if AB=CD, and CD=EF, then AB=EF.

--Angle Measure-- For any angles <A, <B, and <C, if m<A=m<B and m<B=m<C, then m<A=m<C

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Conjecture

An unproven statement that is based on observations.

EXAMPLE: Conjecture: All prime numbers are odd.

Educated guess

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Inductive Reasoning

The process of arriving at a conclusion based on a set of observations or examples

EXAMPLE: Given the number pattern 1,5,9,13,..., you can use inductive reasoning to determine that the next number in the pattern in 17.

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Counterexample

A specific case that shows a conjecture is false.

EXAMPLE: All prime numbers are odd.

Counterexample: 2, a prime number that is not odd.

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Conditional Statement

A logical statement that has two parts, if/then

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Hypothesis

It's what logically comes first after the "if". The "p" of a conditional statement.

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Conclusion

It is what logically comes second after the "then". The "q" of a conditional statement.

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Contrapositive

If ~q, then ~p.

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Logically Equivalent Statements

Two statements that are both True or both False. They both have the same truth value.

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Perpendicular Lines

Lines that intersect at 90 degrees

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Angle Congruence Postulate

Two angles are congruent if and only if their measures are equal.

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Segment Congruence Postulate

Two segments are congruent if and only if they have the same length.

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Supplement Theorem

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

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Ray

One endpoint and all the points of the line on the one side of the endpoint. EXAMPLE: Ray AB (The endpoint is always listed first.)

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Opposite Rays

Two collinear rays with the same endpoint. EXAMPLE: Ray AB and Ray AC (The endpoints are the same, ray go in opposite directions.)

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Definition of Right Angles

If Angle 1 is a right angle

then m Angle 1= 90 degrees

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Definition of Perpendicular Lines

If Line l is perpendicular to line k,

then m<1=m<2=m<3=m<4=90

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Definition of Supplementary Angles

If m<1+m<2 = 180

then <1 is supp. to <2

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Definition of Complementary Angles

If m<1+m<2 = 90

then, <1 is comp. to <2

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Definition of Congruent Angles

If <1 is congruent to <2

then m<1=m<2

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Definition of Segment Bisector

If AB bisects XY at A

then XA=AY

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Definition of Angle Bisector

If BD bisects <ABC

then m<ABD=m<DBC

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Definition of a Midpoint

If M is the midpoint of AB

then AM=MB

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Two angles supplementary to the same angle or to congruent angles are congruent

If <1 supp. <2 and <2 supp. <3

then <1 is congruent <3

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Two angles complementary to the same angle or to congruent angles are congruent

If <1 comp. <2 and <2 comp. <3

then <1 is congruent <3

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All right angles are congruent

If <1 and <2 are right angles

then <1 is congruent <2

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Vertical Angles are Congruent

If Angle 1 is opposite to angle 2

then <1 is congruent <2

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Angle Addition Postulate

m<ABD+m<DBC= m<ABC

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Segment Addition Postulate

XY+YZ=XZ

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Linear Pair Postulate

If <1 and <2 are adjacent and supplementary

then m<1+m<2=180

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Theorem

A statement that must be proved using undefined terms, definitions, postulates or other proven theorems

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Postulate

A statement that is widely accepted without proof.

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Deductive Reasoning

The process by which a person makes conclusions based on previously known facts, definitions, or rules.

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