MATH 3RD QUARTER

• LINEAR INEQUALITIES - Is a statement of an order relationship
• Relations: “connection” “by pair”
• One - to - one : one term in X is paired to one term in Y (nothing repeats)
• Many - to - one: Many terms in X is paired to one term in Y
• One - to -many: One term in X is paired to many terms in Y
• Logic = “critical thinking” A science that deals with the rules and tests the sound thinking and “proof” by REASONING
• Proof = logical argument in which each statement you make is backed up by a statement that is accepted true
• MATHEMATICAL SYSTEM: A set of structures designed to provide order and procedural operation in a certain discipline
• AXIOMATIC STRUCTURE: refers to any set of axioms from which other axioms can be used in conjunction with derived theorems
• POINTS: most basic term. Has no length, width or thickness. Represented by a DOT
• LINES: no width no thickness but its length extends in one dimension and without an end in both directions
• PLANES: has length and width but no thickness. A flat surface that extends INFINITELY in ALL directions
• Collinear points are points that LIE on the same LINE
• Coplanar points are points that LIE on the same PLANE
• SEGMENT: The union of points A and B and all the points BETWEEN THEM
• SUPPLEMENTARY ANGLES: Two angles that have a sum of 180 degrees
• COMPLEMENTARY ANGLES: Two angles that have a sum of 90 degrees
• CONGRUENT ANGLES: Two angles that have equal measure
• LINEAR PAIRS: They are ADJACENT ANGLES and THEIR UNCOMMON SIDES ARE OPPOSITE RAYS
• VERTICAL ANGLES: Non-Adjacent and formed by TWO INTERSECTING LINES
• POSTULATE - are statements accepted as true WITHOUT PROOF
• THEOREMS - statements that need to be PROVEN
• COROLLARY - a theorem that is a DIRECT CONSEQUENCE of another theorem
• LEMMA - A theorem used as a STEPPING STONE
• LINE POSTULATE: Two points contained in one and only one line
• PLANE POSTULATE: Three non-collinear points contained in one and only one plane
• FLAT-PLANE POSTULATE: Two points are in a plane then the line containing these points are in the same plane
• LINE-INTERSECTION POSTULATE: Two lines intersect then their intersection is a POINT
• PLANE-INTERSECTION POSTULATE: If two planes intersect their intersection is a LINE
• LINE-POINT THEOREM: If there is a line and a point not on the line then there is exactly one plane that contains them
• MIDPOINT THEOREM: Point M is the Midpoint of Line AB if and only if AM = MB = ½ AB