Addition Properties
| Question (memorize) | Answer (memorize) |
|---|---|
| closure | a + b is unique real number |
| commutative | a + b = b + a |
| associative | (a + b) + c = a + (b + c) |
| additive of zero | a + 0 = a and 0 + a = a |
| additive inverses | a + (-a) = 0 and (-a) + a = 0 |
Multiplication Properties
| Question (memorize) | Answer (memorize) |
|---|---|
| closure | a * b is a unique real number |
| commutative | ab = ba |
| associative | (ab)c = a(bc) |
| multiplication postulate of one | a * 1 = a and 1 * a = a |
| multiplicative inverses | a * 1/a = 1 |
| distributive | a(b + c) = ab + ac and (b + c)a = ba + ca |
Equality and Inequality
| Question (memorize) | Answer (memorize) |
|---|---|
| reflexive | a = a |
| symmetric | if a = b, b = a |
| transitive | if a = b and b = c, then a = c |
| comparison | only one is true: a < b, a = b, b < a |
| transitive postulate | if a < b and b < c, then a < c |
| additive postulate | if a < b, then a + c < b + c |
| multiplicative postulate | if a < b and 0 < c, then ac < bc; if a < b and c < 0, then bc < ac |
Proved Properties (Theorems)
| Question (memorize) | Answer (memorize) |
|---|---|
| Addition (equality) | if a = b, then a c = b + c and c + a = c + b |
| Subtraction (equality) | if a = b, then a - c = b - c and c - a = c - b |
| Multiplication (equality) | if a = b then ac = bc |
| Division (equality) | if a = b, and c ≠ 0, then a/c = b/c |
| Subtraction (inequality) | if a < b, then a - c < b - c and c - a < c - b |
| Division (inequality) | if a < b, and c > 0, then a/c < b/c if a < b, and c < 0, then a/c > b/c |
| Substitution Principle | if a = b, a can be replaced by b |
| Zero-Product Property | if ab = 0, then a = 0 or b = 0 |
Postulates
| Question (memorize) | Answer (memorize) |
|---|---|
| P1 | a line contains at least two points a plane contains at least three points not all on one line space contains at least 4 points not all in one plane |
| P2 | through any two different points, there is exactly one line |
| P3 | through any three points which are not on one line, there is exactly one plane |
| P4 | if two points lie in a plane, then the line containing them lies in that plane |
| P5 | if two different planes intersect, then their intersection is a line |
| P6 | Between any 2 points ther is a unique distance |
| P7 | (Ruler Postulate) AB= lx-yl and there is a one-to-one correspondence with all real numbers and points on the number line |
Theorems
| Question (memorize) | Answer (memorize) |
|---|---|
| Theorem 3-1 | If 2 lines intersect, they intersect at exactly one point |
| Thoerem 3-2 | If a point lies oustide a line, exactly one plane contains the point and line |
| Thoerem 3-3 | if 2 lines itersect, only one plane contains both lines |
| Thoerem 3-4 | On a ray there is exactly one point at a given distance from the ray's endpoint |
| Thoerem 3-5 | A segment has exactly one mid point |
| Pythagorean Theorem | a2 + b2 = c2 in a right triagle when a and b are the legs and c is the hypotenuse |
Add a section to this page!
- Click this button to contribute to this page (by adding a section here).♦
Feel free to experiment. Your edits won't immediately show up to everyone.
working...