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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. |