| A | B |
|---|
| Collinear | Points are "collinear" if and only if there is a line that contains all of them. |
| Coplanar | Points are "coplanar" if and only if there is a plane that contains all of them. |
| Space | "Space" is the set of all points. |
| Geometry | Geometry is the study of the relationships among points, angles, surfaces and solids. |
| Geometry as a Science | Geometry is a "science" in which not only "the answer" is important, but also "HOW" and "WHY" you arrived at that answer. |
| Geometry as Mathematics | Geometry is a mathematical system that uses logical reasoning, building upon known and accepted facts, to discover new properties. |
| Geometric "Definitions" | Geometric "Definitions" are statements describing certain figures and conditions |
| Geometric "Postulates" | Geometric "Postulates" are statements assumed to be TRUE WITHOUT PROOF. |
| Geometric "Theorems" | Geometric "Theorems" ae statements PROVEN ON THE BASIS OF DEFINITIONS, POSTUALTES, AND PREVIOUSLY PROVEN THEOREMS. |
| Point | In Geometry, a "point" is an undefinited term which has a place in space but has NO DEMENSION (no measurement) - it has NO LENGHT NOR ANY THICKNESS. |
| What is a "point" labeled with in Geometry? | In Geometry, a "point" is a "DOT" that is labeled with a "CAPITAL/PRINTED LETTER" of the alphabet. |
| Line | In Geometry, a "line" is a SET OF POINTS with LENGHT but NO THICKNESS; therefore, it is ONE DEMESIONAL. - a line GOES ON INDEFINITELY IN EITHER DIRECTION. |
| What is the "symboL" for a "line" in Geometry? | <--------> |
| What is a "line" labeled in Geometry? | In Geometry, a "line" is labeled "WITH A LOWER CASE/CURSIVE LETTER" of the alphabet. |
| Plane | A "plane" is an undefined term in Geometry that can be thought of as FLAT SURFACES that EXTEND INDEFINITELY in all directions and have NO THICKNESS; therefore, a "plane" has "TWO(2) DEMENSIONS" which are "LENGHT" and "WIDTH". |
| What is a "plane" labeled with in Geometry? | In Geometry, a "plane" is labeled with a "SINGLE CAPITAL/PRINTED LETTER" of the alphabet. |
| What are "real numbers" used for in Geometry? | In Geometry, "REAL NUMBERS" are used to "EXPRESS SIZE and DISTANCE" - "REAL NUMBERS" are made up of "COUNTING NUMBERS (all positive whole numbers except "zero), WHOLE NUMBERS (all positive whole number including zero), INTEGERS (all positive and negative counting numbers including zero), RATIONAL NUMBERS (all fractions and "repeating decimals"), and IRRATIONAL NUMBERS (all positive "radicial numbers (number under a radical sign) that have "nonrepeating decimals". |
| Coordinate | A "coordinate" is a number associated with "A POINT ON A NUMBER LINE". |
| What is the "absolute value" in Geometry? | In Geometry, the "Absolute Value" of a number is the "DISTANCE OF THAT NUMBER FROM ZERO ON THE NUMBER LINE". |
| What is the "principal square root" in Geometry? | In Geometry, the "principal square root" of a number is its positive square root. |
| Inductive Reasoning | In Geometry, "Inductive Reasoning" is a type of "LOGICAL THINKING" where mathematical statements are "JUSTIFIED BY EXAMPLES". |
| Deductive Reasoning | In Geometry, "Deductive Reasoning" is a "LOGICAL SEQUENCE OF STEPS" justified by "POSULATES, THEOREMS, AND DEFINITIONS" used to PROVE MATHEMATICAL STATEMENTS". |
| Even number | An "Even number" is any number tht can be expressed as 2x, where x is an integer. |
| Odd number | An "Odd number" is any number that can be expressed as 2x + 1 , where x is an integer. |
| Two-Column Proof | In Geometry, a "TWO-COLUMN PROOF", is where "STATEMENTS ARE MADE IN ONE COLUMN" and are "JUSTIFIED IN THE OTHER" - using "DEDUCTIVE REASONING". |
| What must one do in Geometry to prove a statement "false"? | In Geometry, to PROVE A STATEMENT "FALSE" one need "ONLY "ONE" FALSE EXAMPLE. |
| In Geomtry, can one use "Inductive Reasoning" to prove a "statement true"? | In Geometry, "Inductive Reasoning", or seeing a trend through "MANY EXAMPLES", does "NOT PROVE" many STATEMENTS TRUE. |
| Closure property of addition and multiplication | a + b is a real number; a x b is a real number |
| Commutative property of addition and multiplication | a + b = b + a; a x b = b x a |
| Associative propertY of addition and multiplication | ( a + b) + c = a + (b+c); (a x b) x c = a x (b x c) |
| Identity property of addition | a + 0 = a |
| Identity property of multiplication | a x 1 = a |
| Inverse property of addition | a + (-a) = 0 |
| Multiplicative property of zero | a x 0 = 0 |
| Inverse property of multiplication | a x 1/a = 1 |
| Distributive property of multiplication over addition | a x (b + c) = (a x b) + (a x c) |
| Reflexive property of equality | a = a |
| Symmetric property of equality | If a = b, then b = a |
| Transitive property of equality | If a = b and b = c, then a = c |
| Substitution propeerty | If a = b, then "a" may be substituted for "b" |
| Addition property of equality | If a = b, then a + c = b + c |
| Subtraction property | a - b = a + (-b) |
| Subtraction property of equaltiy | If a = b, then a - c = b - c |
| Multiplication property of equality | If a = b, then c x a = c x b |
| Division property of equality | If a = b and c does not equal 0, then a/c = b/c} |
| Transversals: Alternate Interior Anges | are congruent |
| Transversals: Corresponding Angles | Are congruent |
| Transversals: Opposite or Vertical Angles | Are congruent |
| Transversals: Interior Angles | Angles between the parallel lines |
| Transversals: Exterior Angles | Angles outside the parallel lines |
| Transversal | A slanted line crossing through two(2) parallel lines |
| Acute Angle | An angle between 0 and 90 degrees |
| Strainght Angle | A 180 degree angle |
| Obtuse Angle | An angle between 90 and 180 degrees |
| Reflex Angle | An angle between 180 and 360 degrees |
| Right Angle | A 90 degree angle |
| Complementary Angles | Two(2) angles whose measures add up to 90 degrees |
| Supplementary Angles | Two(2) angles whose measures add up to 180 degrees |
| Bisector | To divided into "two(2) equal parts" |
| Angle Bisector | To divide an angle into two(2) equal parts |
| Line Bisector | To divide a line into two(2) equal parts |
| Intersecting Lines | Two(2) lines that intersect at "one point" within a plane |
| Perpendicular | To form "right angles" |
| Perpendicular Lines | Two(2) lines that intersect to form two(2) right angles |
| Perpendicula Bisector | A line that intersect another line and divides it into two(2) equal parts and also forms "two(2) right angles" |
| Ray | A "ray" has an end point on one end and goes on indefinitely on the other end |
| Angle | An "angle" has two(2) (which are rays) and a vertex |
| Vertex of an Angle | The "vertex of an angle" is where the two(2) sides (rays) of an angle meet to form the interior of the angle |
| Line Segment | it has two(2) end points |
In angle | B | |
