chapter 3 Flashcards
parallel lines
two lines are parallel if they are coplanar and do not intersect
intersecting lines
intersecting lines are coplanar and have exactly one point in common
oblique lines
lines are oblique if they intersect and do not form a right angle
skew lines
two lines are skew if they do not lie in the same plane
thm 3.1: transitive property of parallel lines
if 2 lines are parallel to the same line, then they are parallel to each other.
thm 3.2: property of perpendicular lines
if two coplanar lines are perpendicular to the same line, then they are parallel to each other
thm 3.4
all right angles are congruent
thm 3.3
if two lines are perpendicular, then they intersect to form 4 right angles
thm 3.5
if 2 lines intersect to form a pair of adjacent congruent angles, then the two lines are perpendicular
transversal
a transversal is a line that intersects two or more coplanar lines at different points
corresponding angles
2 angles are corresponding angles if they occupy corresponding positions,
alternate interior angles
2 angles are alternate interior angles if they lie between (cursive) l and m on opposite sides of t.
alternate exterior angles
2 angles are alternate exterior angles if they lie outside (cursive) l and m on opposite sides of t.
consecutive interior angles
2 angles are consecutive interior angles if they lie between (cursive) l and m on the same side of t
corresponding angles postulate
if 2 parallel lines are cut by transversal, then the pairs of corresponding angles are congruent
alternate interior angles theorum
if 2 parallel lines are cut by a transversal, then the pairs of alt. int. angles are congruent.
consecutive interior angles theorum
if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
alternate exterior angles theorum
if 2 parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
perpendicular transversal theorum
if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the second.
Postulate 12
if two distinct lines intersect, then their intersection is exactly 1 point
Parallel postulate
If their is 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.
Corresponding angles converse postulate
if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
alt. int. angles converse thm.
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel
consec. int. angles converse thm.
if 2 lines are cut by a transversal so that consec. int. angles are suppl., then the lines are parallel.
alt. ext. angles coverse thm.
if 2 lines are cut by a transversal so that alt. ext. angles are congruent, then the lines are parallel.
