Math Chapter One Notes

Concepts and Procedures Should Be Able To... 1.1: Define all listed Vocabulary Recognize in context1.2: Measure segments and angles Classify angles and name the parts of a degree Recognize congruent angles and segments1.3: Recognize when a point is between two other points Apply the triangle-inequality principle Correctly interpret geometric diagrams1.4: Write simple two-column proofs1.5: Identify bisectors and trisectors of segments and angles1.6: None Applicable (Paragraph Proofs not used)1.7: Recognize that geometry is based on deductive structure Identify undefined terms, postulates, and definitions Understand the characteristics and application of theorems1.8: Recognize the condition, negation, converse, inverse, and contrapositive of a statement Use the chain rule to solve problems1.9: Solve probability problems Vocabulary angle: made up of two rays with a common endpoint (vertex); the rays are called 'sides' of the anglebisect: the division of a segment into two congruent segments (or angles)chain rule: series of steps in a logical sequence {if p => q, and if q => r, then p => r}collinear: points that lie on the same lineconclusion: the 'then' part of an implicationconditional statement: an 'if...then' statement {if p then q}congruent: identical in form; coinciding exactly when lain on top of one anothercontrapositive: the 'if not, then not' form of converse { if not q then not p}converse: the reversed order of a conditional statement/implication {if q then p}counterexample: an example in which a conclusion is false deductive structure: a system of though in which conclusions are justified by means of previously assumed or proved statementshypothesis: the 'if' part of an implicationimplication: an 'if...then' statementintersection: the vertex of a triangle, the place in which lines or segments meetinverse: the 'if not then not' form of the original statement {if not p then not q}line: made up of points and is straight; extend infinitely in both directionsline segment: made up of points and is straight; has a definite beginning and endmeasure: sizemidpoint: the bisection point of a segmentminute: ' (60' = 1 degree)negation: 'not ____' in a conditional statement; used in the inverse and contrapositivenon-collinear: points that do not lie on the same linenumber line: the case in which a numerical value is assigned to each point on a linepostulate: an unproved assumptionprobability: the likelihood of something happeningray: made of up points and is straight; has an endpoint and extends infinitely in only one directionsecond: " (60" = 1')theorem: a mathematical statement that can be provedtrisect: when two rays divide an angle or segment into three congruent partsunion: the combination of all (a triangle is the union of three segments)Venn Diagram: the utilization of conditional statements and all their forms to compare and contrastvertex: the point of intersection in a triangle