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Geometry Chapter 1
Chapter 1 only
| Term | Definition |
|---|---|
| Point | A dot in space. A location with no dimension. |
| Line | A connected straight path. It has no thickness and continues forever. |
| Plane | A flat surface. It has no thickness but goes on forever. |
| Line Segment | A line but it is bounded by two points. It has no thickness. |
| Ray | A line with a fixed starting point but has no endpoint. |
| Parallel | Two lines that don't intersect on the same plane. |
| Coplanar | Two points on the same plane. |
| Collinear | Two points on the same line. |
| Postulate | A statement believed true without a proof. |
| Segment Addition Postulate | Let A, B and C be 3 collinear points If B is between A&C, then AB+BC= AC |
| Distance Formula | d=√((x_2-x_1)²+(y_2-y_1)²) |
| Midpoint | The point that divides the line segment into two segments of the same length. |
| Segment Bisector | Any line ray or segment that passes through midpoint. |
| Midpoint Formula | (x₁ + x₂)/2, (y₁ + y₂)/2 |
| Angle | A figure formed by two rays. |
| Vertex | Common endpoint of angle. |
| Degrees | Common measurement unit for circular arcs |
| Acute Angle | An angle that is more than 0 degrees but less than 90. |
| Right Angle | An angle that is equal to 90 degrees. |
| Obtuse Angle | An angle that is more than 90 degrees but less than 180. |
| Angle Bisector | A ray that divides an angle into 2 angles of the same measure. |
| Angle Addition Postulate | If point A is in the interior of ∠ SYR then m ∠SYR= m ∠SYA + m ∠RYA |
| Transformation | A function that changes position, size, or shape of a figure. |
| Image | Image after the change |
| Preimage | Image before the change. |
| Rigid motion | Move shape without changing size or shape (translation, reflection, rotation) |
| Conjecture | A statement believed to be true. |
| Inductive reasoning | A type of reasoning that uses specific cases to make a rule of belief that is true. |
| Deductive Reasoning | The process of using logic to prove all cases are true. |
| Theorem | A statement that you can prove using a series of logical steps. |
| Counterexample | An example that shows a conjecture to be false. |
| Addition Property of Equality | If a=b then a + c = b + c |
| Subtraction Property of Equality | If a=b then a - c = b - c |
| Multiplication Property of Equality | If a=b then ac = bc |
| Division Property of Equality | If a=b then a/c=b/c, c can't be 0 |
| Reflexive Property of Equality | A number is always equal to itself, 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 Property of Equality | If a=b then you can substitute b in for a in any expression |
| Linear Pair Theorem | If two angles form a linear pair, then the measures of the angles add up to 180 degrees. |