Chapter 2: Reasoning & Proofs

Law of Detachment: If p ---> q is true and p is true, then q is also true. As long as the fact (p) is true the conclusion (q) will also be true. If q is true and p--->q is also true, then p could be true or false, thus resulting in a no valid concussion. (True by default)

Law of Syllogism: Drawing a conclusion from 2 conditional statements when conclusion of one statement is the hypothesis of other statement. If conclusion of the first statement is not the hypothesis of the second statement then no valid concussion can be drawn.

2.5

Thanks to Amruth Nadiampally

Postulate/Axiom: A postulate or axiom is a statement that is accepted as true without proof. Basic ideas about points, lines, and planes can be stated as postulates.

Postulates: (remember that you don't have to quote the exact number - just the postulate)

2.1 - Through any two points, there is exactly one line.

2.2 - Through any three non collinear points, there is exactly one plane.

2.3 - A line contains at least two points.

2.4 - A plane contains at least three non collinear points.

2.5 - If two points lie in a plane, then the entire line containing those points lies in that plane.

2.6 - If two lines intersect, then their intersection is exactly one point.

2.7 - If two planes intersect, then their intersection is a line.

Proof: A proof is a logical argument in which each statement you make is supported by a statement that is accepted as true.

Paragraph Proof: A paragraph proof involves writing a paragraph to explain why a conjecture for a given situation is true.

Informal Proofs: Paragraph proofs are also called informal proofs, but just because it is called informal, doesn't mean it is any less formal than the other variations of proofs.

2.6

Thanks to Ishwari Veerkar

Addition Property of Equality: if a=b, then a+c = b+c

Subtraction Property of Equality: if a =b, then a-c = b-c

Multiplicative Property of Equality: if a=b then a*c = b*c

Division Property of Equality: if a=b, then a/c = b/c

Reflexive Property: a=a (think of yourself looking in a mirror)

Symmetric Property: if a=b, b=a

Transitive Property: if a=b and b=c then a=c

DIstributive: a(b+c) ---> ab + ac

2.7

Thanks to Ishwari Veerkar

Ruler Postulate: The points on any line or segment can be put into correspondance with real numbers. (Basically if a point is 0 then the other point extending in the right direction has to be a real number)

Segment Addition Postulate: If A,B,C are collinear and B is between A & C then AB+BC=AC(2 segments adding together, resulting in a whole)

2.8

Thanks to Ishwari Veerkar

Angle Addition Postulate: Same as the Segment Addition except angles are used instead of segments.

Supplement Theorem: If 2 angles form a linear pair then they are supplementary.

Complement Theorem: If non common sides of 2 adjacent angles form a right angle then the angles are complementary angles.

Congruent Supplement: If 2 angles are complementary/ supplementary to a same angle then they are congruent.

2 Congruent Supplement: If 2 angles are complementary/ supplementary to 2 same angles then they are congruent.