highschool geometry, algebra 2, triginometry, pre-calc/calculus
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92 terms
Terms | Definitions |
|---|---|
 undefined term | A word without a formal definition. |
| point | A point has no dimension. It is represented by a dot. |
| line | A line has one dimension. It is represented by a line with two arrowheads. |
| plane | A plane has two dimensions. It is represented by a shape that looks like a floor or a wall. |
| collinear points | Points that lie on the same line. |
| coplanar points | Points that lie in the same plane. |
| defined terms | Terms that can be described using known words. |
| line segment/endpoints | Part of a line that consists of two points, called endpoints, and all the points on the line between the endpoints. |
| ray | The ray "AB" consists of the endpoint "A" and all points on line "AB" that lie on the same side of "A" as "B." |
| opposite rays | 2 rays that have the same endpoint and go in opposite directions forming a line. |
| postulate, axiom | A rule that is excepted withought proof. |
| theorem | A rule that can be proved. |
| coordinate | The real number that corresponds to a point. |
| distance | The distance between two points "A" and "B," written as "AB," is the absolute value of the difference of the coordinates of "A" and"B." |
| between | When three points are collinear, you can say that one point is between the other two. |
| congruent segments | Line segments that have the same length. |
| segment addition postulate | AB + BC = AC. |
| complementary angles | 2 angles whose sum is 90 degrees. |
| supplementary angles | two angles whose sum is 180 degrees. |
| adjacent angles | two angles that share a common vertex or side, but have no common interior points. |
| linear pair | two adjacent angles are a linear pair if their noncommon sides are opposite rays. |
| vertical angles | two angles are vertical angles if their sides form two pairs of opposite rays. |
| conjecture | an unproven statement that is based on observations. |
| inductive reason | the process of finding a pattern for specific cases and then writing a conjecture for the general case. |
| counterexample | a specific case for which the conjecture is false. |
| conditional statement | a logical statement that has 2 parts: a hypothesis and a conclusion. |
| if-then-form | a form of a conditional statement in which the "if" part contains the hypothesis and the "then" part contains the conclusion. |
| hypothesis | the "if" part of a conditional statement. |
| conclusion | the "then" part of a conditional statement. |
| negation | the opposite of the original statement. |
| converse | the part of a conditional statement that is formed by negating both the hypothesis and conclusion. |
| inverse | the part thats formed by negating both the hypothesis and the conclusion. |
| contra-positive | the part that is formed by writing the converse and then negating both the hypothesis and the conclusion. |
| equivelent statements | 2 statements that are both true or both false. |
| perpendicular lines | 2 lines that intersect to form a right angle. |
| biconditional statement | a statement that contains the phrase "if, and only if" |
| deductive reasoning | using facts, definitions, excepted properties, and laws of logic to form a logical argument. |
| line perpendicular to a plane | if, and only if, the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point. |
| postulate 1: | through any two points there exists exactly one line |
| postulate 2: | a line contains at least 2 points |
| postulate 3: | if 2 lines intersect, then their intersection is exactly one point |
| postulate 4: | ~postulate #4 was executed before its people and sadly, no longer exists :( |
| postulate 5: | through any 3 noncollinear points there exists exactly one plane |
| postulate 6: | a plane contains at least 3 noncollinear points |
| postulate 7: | if 2 points lie in a plane then the line containing them [also] lies in the plane |
| postulate 8: | if two planes intersect, then their intersection is a line |
| postulate 11 1/2: (don't ask me how) | through any 3 noncollinear points, there exists exactly one plane |
| addition property | if a = b, then a+c = b+c. |
| subtraction property | if a = b, then a - c = b - c. |
| multiplication property | if a = b, then a x c = b x c. |
| division property | if a = b, then a\c = b\c. |
| substitution property | if a = b, then "a" can be subbed for "b" |
| proof | A logical argument that shows a statement is true. |
| two-column proof | Has numbered statements and corresponding reasons that show an argument in logical order. |
| Theorem | a statement that can be proven |
| parallel lines | two lines that do not intersect and are co-planar |
| skew lines | two lines that do not intersect and are NOT coplanar |
| parallel planes | two planes that do not intersect |
| transversal | a line that intersects two or more coplanar lines at different points |
| corresponding angles | two angles that have corresponding positions |
| alternate interior angles | two angles that lie between the two lines and on opposite sides of the transversal |
| alternate exterior angles | two angles that lie outside the two lines and on opposite sides of the transversal |
| consecutive interior angle | two angles that lie between the two lines and on the same side of the transversal |
| postulate 15: | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |
| slope-intercept form | the general form of a linear equation in slope-intercept form is 'y=mx+b' where "m" is the slope and "b" is the Y-intercept |
| standard form | the general form of a linear equation in standard form is Ax+By=c, where "A" and "B" are not both zero |
| distance from a point to a line | the length of the perpendicular segment from the point to the line |
| triangle | a polygon with 3 sides |
| interior angles | when the sides of a polygon are extended, the original angles are the interior angles |
| exterior angles | when the sides of a polygon are extended, the angles that form linear pairs with the interior angles are the exterior angles |
| corollary to a theorem | a statement that can be proved easily using a theorem |
| congruent figures | where all the parts of one figure are congruent to the corresponding parts of the other figure |
| corresponding parts | in congruent polygons, the corresponding parts are the corresponding sides and the corresponding angles |
| leg of a right triangle | in a right triangle, a side adjacent the right angle is called a leg |
| hypotenuse | in a right triangle, the side opposite the right angle is called the hypotenuse |
| flow proof... | DONT CARE...... |
| legs | the two congruent sides of an isosceles triangle |
| vertex angle | the angle formed by the legs in an isosceles triangle |
| base | the side of an isosceles triangle that is not a leg |
| base angles | the two isosceles angles congruent to the base |
| transformation | an operation that moves or changes a geometric figure in some way to produce a new figure |
| image | the new figure produced by a transformation |
| translation | moves every point of a figure the same distance in the same direction |
| reflection | uses a "LINE OF REFLECTION" to create a mirror image of the original figure |
| rotation | turns a figure about a fixed print, called the "CENTER OF ROTATION" |
| midsegment of a triangle | a segment that connects the midpoints of two sides of a triangle |
| coordinate proof | involves placing geometric figures in a coordinate plane |
| perpendicular bisector | a segment, ray, line, or plane that is perpendicular to a segment at its midpoint |
| equidistant | if a point is the same distance between each two figures |
| concurrent | when three or more lines/rays or segments intersect in the same point |
| point of concurrency | the point of intersection of concurrent lines, rays, or segments. |
| circumcenter | the point of concurrency of the three bisectors of a triangle |
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