Chapter 3 Flashcards
Parallel Lines
Coplanar lines that do not intersect.
Intersecting Lines
Coplanar lines that have exactly one point in common.
Oblique Lines
Intersecting lines that are not perpendicular.
Skew Lines
Two lines that do not lie in the same plane.
Theorem 3.1 Transitivity of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other.
Theorem 3.2 Property of Perpendicular Lines
If two coplanar lines are perpendicular to the same line, then they are parallel to each other.
Postulate 12
If two distinct lines intersect, then their intersection is exactly one point.
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.
Negation
Denial of a statement.
Contrapositive
If we have a conditional statement: “If p, then q,” then the contrapositive is written as: ‘If ~q, then ~ p.”
Transversal
A line that intersects two or more coplanar lines at different points.
Corresponding Angles
Two angles that occupy corresponding positions.
Alternate Interior Angles
Two angles that lie between l and m, on opposite sides of t
Alternate Exterior Angles
Two angles that lie outside l and m, on opposite sides of t.
Consecutive Interior Angles
Two angles that lie between I and m on the same side of t
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Alternate Angles Theorem
Of two parallel lines are cut by a transversal, then the pairs if alternate interior angles are congruent.
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal; then the pairs if consecutive interior angles are supplementary.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal,then the pairs of alternate exterior angles are congruent.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the second.
