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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
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