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# Geometry

### Postulates, Theorems & Definitions

Question | Answer |
---|---|

Congruent segments | Line segments that have the exact same length, shape or size. |

Postulate #1: Ruler postulate | The distance between one point to another (absolute value) [x2 - x1] |

Postulate #2: Segment addition postulate | If B is between A and C, then AB+BC=AC |

Postulate #3: Protractor Postulate | When you line up a protractor at 0 degrees, the angle measure lines up with that on the protractor |

Postulate #4: Angle addition postulate | If D is the interior of <ABC, then <ABD+<DBC+<ABC |

Postulate #5: | through any 2 points there exists exactly one line |

Postulate #6 | A line contains at least 2 points |

Postulate #7 | If 2 lines intersect, then there intersection is exactly one point |

Postulate #8 | through any 3 noncollinear points there exists exactly one plane |

Postulate #9 | A plane contains at least three noncollinear points |

Postulate #10 | if 2 points lie on a plane, then the line they lie on lies on the plane |

Postulate #11 | If 2 planes intersect, then there intersection is a line |

Postulate #12: Linear Pair Postulate | If 2 angles are a linear pair, then they are supplementary |

Midpoint | Point that divides a segment into 2 congruent segments |

Segment Bisector | a point, ray, line, line segment, or plane that intersects the segment at its midpoint. |

Right angle | measure of angle = 90 degrees |

Straight angle | measure of angle = 180 degrees |

Acute angle | Measure of angle is less than 90 degrees, and more than 0 |

Obtuse angle | Measure of angle is greater than 90 degrees, but less than 180 degrees |

Congruent angles | Angles with the exact same measurement |

Angle Bisector | A ray that divides an angle into 2 congruent angles |

Complementary Angles | The sum of 2 angles is 90 degrees |

Supplementary Angles | 2 angles with the sum of 180 degrees |

Adjacent Angles | Share a common side and vertex, no interior point |

Linear pair | If there non common sides are opposite rays |

Vertical Angles | The sides form 2 pairs of opposite rays |

Conjecture | An unproven statement based on observation |

Inductive reasoning | When you find a pattern in specific cases, write a conjecture |

Counterexample | A specific example/case proving the conjecture wrong |

Conditional Statement | A logical statement that has 2 parts, a hypothesis and a conclusion |

If-then form | If hypothesis, then conclusion. "If A, then B" |

Converse | If conclusion, then hypothesis. |

Inverse | If not The hypothesis, then not the conclusion |

Contrapositive | If not the conclusion, then not the hypothesis |

Biconditional statement | If and only if... |

Negation | the opposite of the original statement. |

Equivalent statement | When 2 statements are both true and both false |

Perpendicular lines | 2 lines intersect and form a right angle |

Law of detachment | If the converse is true then the conclusion is also true |

Law of syllogism | If a, then b. If b, then c. If A, then c. |

Substitution Property | If a=b, then a can be substituted for b in any equation or expression |

Distributive property | a(b+c) = ab+ac |

Do the reflexive, symmetric, and transitive properties of equality pertain to measurement of angles and segments or congruence? | The properties of equality pertain to measurements |

Theorem 2.1: Congruence of segments | Is reflexive, symmetric, and transitive. Pertains to congruence |

Theorem 2.2: Congruence of angles | Is reflexive, symmetric, and transitive. Pertains to congruence (Symmetric property of segment congruence) |

Theorem 2.3: Right angles congruence theorem | All right angles are congruent |

Theorem 2.4: Congruent supplements theorem | If 2 angles are supplementary to the same angle, then they are congruent |

Theorem 2.5: Congruent complements theorem | If 2 angles are complementary to the same angle, then they are congruent |

Theorem 2.6: Vertical Angles congruence theorem | Vertical angles are congruent |

Created by:
jill_genova