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Geometry 3.1-3.6
| Term | Definition |
|---|---|
| Parallel Lines | two lines that do not intersect and are coplanar |
| Skew Lines | two lines that do not intersect and are not coplanar |
| Parallel Plane | two planes that do not intersect |
| Parallel Postulate | if there is a line and a point not on the line then there is exactly one line through the point parallel to the given line |
| Perpendicular Postulate | if there is a line and a point not on the line then there is exactly one line through the point perpendicular to the given line. |
| Transversal | a line that intersects two or more coplanar lines at different points |
| Corresponding angles | two angles with corresponding positions and are above the lines and to the right of the transversal |
| Alternate interior angles | two angles that lie between the two lines and on opposite sides of the transversal |
| Alternate exterior angles | if two angles lie outside the two lines and on opposite sides of the transversal |
| Consecutive interior angles | two angles that lie between the two lines and on the same side of the transversal |
| Corresponding angles postulate | if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent |
| Alternate interior angles theorem | if two parallel lines are cut by transversal, then the pairs of alternate interior angles are congruent |
| Alternate exterior angles theorem | if two parallel lines are cut by transversal, then the pairs of alternate exterior angles are congruent |
| Consecutive interior angles theorem | if two parallel lines are cut by transversal, the the pairs of consecutive interior angles are supplementary |
| Corresponding angles converse | if two lines are cut by transversal so the corresponding angles are congruent, then the lines are parallel |
| Alternate interior angles converse | if two lines are cut by transversal so the alternate interior anfles are congruent then the lines are parallel |
| Alternate exterior angles converse | if two lines are cut by transversal so the alternate exterior angles are congruent, then the lines are parallel |
| Consecutive interior angles converse | if two lines are cut by transversal so the consecutive interior angles are supplementary then the lines are parallel |
| Paragraph proof | a proof written in a paragraph, the statements and response in a paragraph proof are written in sentences using worlds to explain the logical flow of the argument |
| Transitive property of parallel lines | if two lines are parallel to the same lines then they are parallel to each other |
| slope | non-vertical line is the ratio of vertical change (rise) to horizontal change (run) between any two points on the line |
| slope of parallel lines | in a coordinate plane, two non vertical lines re parallel if and only if they have the same slope. Any two vertical lines are parallel |
| slopes of perpendicular lines | in a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slope is -1. horizontal lines are perpendicular to vertical lines |
| slope--intersect form | y=mx+b * m=the slope * * b=the y-intercept * |
| standard form | Ax+By=C * A & B both are NOT 0 * |
| theorem 3.8 | if two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular |
| theorem 3.9 | if two lines are perpendicular then they intersect to form four right angles |
| theorem 3.10 | if two sides of two adjacent acute angles are perpendicular then the angles are complementary |
| perpendicular transversal theorem | if a transversal is perpendicular to on of two parallel lines then it is perpendicular to the other |
| lines perpendicular to a transversal theorem | in a plane, if two lines are perpendicular to the same line, then they are parallel to each other |
| distance from a point to a line | the length of a perpendicular segment from the point to the line. This is the shortest distance between the point and the line. |
Created by:
ltopp