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--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
--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
--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
An unproven statement that is based on observations.
EXAMPLE: Conjecture: All prime numbers are odd.
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.
A specific case that shows a conjecture is false.
EXAMPLE: All prime numbers are odd.
Counterexample: 2, a prime number that is not odd.
Logically Equivalent Statements
Two statements that are both True or both False. They both have the same truth value.
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.)
Two collinear rays with the same endpoint. EXAMPLE: Ray AB and Ray AC (The endpoints are the same, ray go in opposite directions.)
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
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
A statement that must be proved using undefined terms, definitions, postulates or other proven theorems
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