Math Chapter One Notes

Page 1

Concepts and Procedures Should Be Able To... 1.1: Define all listed Vocabulary

Recognize in context

1.2: Measure segments and angles

Classify angles and name the parts of a degree

Recognize congruent angles and segments

1.3: Recognize when a point is between two other points

Apply the triangle-inequality principle

Correctly interpret geometric diagrams

1.4: Write simple two-column proofs

1.5: Identify bisectors and trisectors of segments and angles

1.6: 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 theorems

1.8: Recognize the condition, negation, converse, inverse, and contrapositive of a statement

Use the chain rule to solve problems

1.9: Solve probability problems

Vocabulary angle: made up of two rays with a common endpoint (vertex); the rays are called 'sides' of the angle

bisect: 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 line

conclusion: the 'then' part of an implication

conditional statement: an 'if...then' statement {if p then q}

congruent: identical in form; coinciding exactly when lain on top of one another

contrapositive: 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 statements

hypothesis: the 'if' part of an implication

implication: an 'if...then' statement

intersection: the vertex of a triangle, the place in which lines or segments meet

inverse: 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 directions

line segment: made up of points and is straight; has a definite beginning and end

measure: size

midpoint: the bisection point of a segment

minute: ' (60' = 1 degree)

negation: 'not ____' in a conditional statement; used in the inverse and contrapositive

non-collinear: points that do not lie on the same line

number line: the case in which a numerical value is assigned to each point on a line

postulate: an unproved assumption

probability: the likelihood of something happening

ray: made of up points and is straight; has an endpoint and extends infinitely in only one direction

second: " (60" = 1')

theorem: a mathematical statement that can be proved

trisect: when two rays divide an angle or segment into three congruent parts

union: 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 contrast

vertex: the point of intersection in a triangle