Test Issue 10

https://docs.google.com/document/d/12mcDyVOZg4fjiCXYkjOEgQRbeAznuBLU9-cXtXU9V0g/edit
3.01.12 ISSUE 10: Math Definitions Geometry
Made by: Miyu

Generalization: A reference from using a few tries
Inductive Reasoning: A method of reasoning in which a series of particular example leads to a conclusion
Counterexamples: A false example of an generalization
Conjecture: Statements that are likely to be true but not yet been proven true by deductive proof
Deductive Reasoning: Using the logic to combine definitions and general statements that we know to be true to reach a valid conclusion
Given: The information known to be true
Prove: The conclusion
Two- Column Proof: The left column, you write Statements that we know to be true and in the right column, you write Reasons why the statement is true
Paragraph Proof: Each statement must be justified by stating a definition or another statement that has been accepted or proved to be true.
Direct Proof: A proof that starts with the given statements and uses the laws of logic to arrive at the statement to be proved
Indirect Proof: A proof that starts with the negation of the statement to be proved and uses the laws of logic to show that it is false. This is also known as Proof By Contradiction
Postulate/ Axiom: Statements that seems so obvious that we accept them without proof
Theorem: A statement that is proved by deductive reasoning
Reflexive Property of Equality: A quantity equal to itself
Symmetric Property of Equality: An equality may be expressed in either order
Transitive Property of Equality: Quantities equal to the same quantity are equal to each other
Equivalence Relation: A relation for which these postulates are said to be true
Substitution Postulate: A quantity may be replaced for its equal in any statement of equality
Partition Postulate: A whole is equal to the sum of all its parts
Postulate 3.5.1: A segment is congruent to the sum of all its parts
Postulate 3.5.2: A angle is congruent to the sum of all its parts
Addition Postulate: If a=b and c=d, then a+c=b+d. If equal quantities are added to equal quantities, the sums are equal
Postulate 3.6.1: If congruent segments are added to congruent segments, the sums are congruent.
Angle Addition Postulate: If congruent angles are added to congruent angles, the sums are congruent
Subtraction Postulate: a=b and c=d, then a-c=b-d, If equal quantities are subtracted from equal quantities, the differences are equal.
Postulate 3.7.1: If congruent statement are subtracted from congruent segments, the differences are congruent
Postulate 3.7.2: If congruent statement are subtracted from congruent angles, the difference are congruent
Multiplication Postulate: If a=b, and c=d, then ac=bd. If equals are multiplied by equals, the products are equal
Postulate 3.9: Doubles of equal quantities are equal.
Division Postulate: If a=b, and c=d, then a/c = b/d. (c=/= 0 and d=/= 0) If equals are divided by nonzero equals, the quotients are equal
Postulate 3.11: Halves of equal quantitiies are equal.
Power Postulate: If a=b, then a^2 =b^2. The squares of equal quantities are equal.
Root Postulate: If a=b and a>0, then radical a =radical b
Postulate 3.13: Postivie Square Roots of postive equals quantities are equal