
Define: Conjecture
an unproven statement that is based on observations

Define: Inductive reasoning
when you find a pattern in specific cases and then wright a conjecture for the general cause

Define: Counterexample
a specific case for which the conjecture is false

what is the counterexample in...
2x>x

Define: conditional statement
 a logical statement that has 2 parts, a hypothesis and a conclusion. It is written in a
 ifthen form

Define: biconditional statements
a statement that contains the phrase "if and only if"
 Example: an angle is a right angle if and only if its angle measurement is equal to
 90 degrees

Define: law of syllogism
 if hypothesis A, then conclusion B
 if hypothesis B, then conclusion C
 if hypothesis A, then conclusion C

Define: law of detachment
Law of Detachment ( also known as Modus Ponens (MP) ) says that if p=>q is true and p is true, then q must be true.
 example:If an angle is obtuse, then it cannot be acute.
 Angle A is obtuse.
 ThereforeAngle A cannot be acute.

Postulate 1: ruler postulate
The points of a line can be matched one to one with the real numbers. The real numbers that correspond to a point is the coordinate

Postulate 2: segment addition postulate
 If B is between A and C, then AB+BC=AC
 If AB+BC=AC, then B is between A and C

Postulate 4: angle addition postulate
If P is in the interion of <RST, then the measure of <T=RST is equal to the sum of the measure of <RSP and <PST

Postulate 5
Through any two points there exists exactly one line

Postulate 6
A line contains at least two points

Postulate 7
If two lines intersect, then their intersection is exactly one point

Postulate 8
through any three noncolinear points there exists exactly one plane

Postulate 9
A plane contains at least three noncolinear points

Postulate 10
If two points lie in a plane, then the line containing them lies in the plane

Postulate 11
If two planes intersect, then their intersection is a line

Define: line perpendicular to a plane
a line perpendicular to a plane if and only if the three line intersects in a point ane is perpendicular to every line in that planethat intersects it at that point

Addition Property
If a=b, then a+c=b+c

subtraction property
If a=b, then ac=bc

multiplication property
If a=b, then ac=ab

division property
If a=b and c is not equal to 0, then a/c=b/c

Subsitution property
If A=b, then "A" can be subsituted for b in any equation or expression

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


Symmetric property
If a=b, then b=a

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

Theorm 2.3: Right angles congruence theorem
All right angle are congruent

Theorem 2.4: congruent supplements theorem
If two angles are supplementry to the same angle, then they are congruent

Theorem 2.5: congruent complements theorem
If two angles are complementry to the same angle , then they are congruent

Postulate 12: linear pair postulate
If two angles form a linear pair, then they are supplementary

Theorem 2.6: vertical angles congruence theorem
Vertical angles are congruent

