Chapter 3 Flashcards
Intersecting lines
Two lines that are coplanar and have exactly one point in common
Parallel lines
Two lines that are coplanar and do not intersect
Oblique lines
Lines that intersect and do not form right angles
Skew lines
Two lines that do not lie in the same plane
Transitivity of parallel lines
If two lines are parallel to the same line, then they are parallel to each other
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…
If two distinct lines intersect, then their intersection is exactly one point
Parallel postulate
If there is one 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
Theorem 3.3 if two lines are perpendicular,
Then they intersect to form four right angles
Theorem 3.4 all right angles…
Are congruent
Theorem 3.5 if two lines intersect to form a pair of adjacent congruent angles…
Then the lines are perpendicular
Transversal
A line that intersects two or more coplanar lines at different points
Corresponding angles postulate
If two parallel lines are cut by a transversal, then the corresponding angles are congruent
Alternate interior angles theorem
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent
Consecutive interior angles theorem
If two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary
Alternate exterior angles theorem
If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent
Perpendicular transversal theorem
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other
Postulate 16 if two lines are cut by a transversal so that corresponding angles are congruent…
The lines are parallel
Alternate interior angles converse
If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel
Consecutive interior angles converse
If two lines are cut by a transversal so that the consecutive interior angles are supplementary, the lines are parallel
Alternate exterior angles converse
If two lines are cut by a transversal so that the alternate exterior angles are congruent, the lines are parallel
