Chapters 3-4 Flashcards
lines that do not intersect and are not coplanar
skew lines
coplanar lines that do not intersect
parallel lines
planes that do not intersect
parallel planes
a line that intersects 2 or more coplanar lines at 2 different points
transversal
the angles on the inside of the transversal pair of angles
interior anges
angles on the outside of the transversal pair of angles
exterior angles
interior angles that lie on the same side of he transversal
consecutive interior angles
nonadjacent interior angles that lie on opposite sides of the transversal
alternate interior angles
nonadjacent exterior angles that lie on the opposite sides of the transversal
alternate exterior angles
angles that lie on the same side of the transversal and on the same side of 2 lines
corresponding angles
if two parallel lines are cut by a transversal then each pair of corresponding angles is congruent
corresponding angles postulate
if two parallel angles are cut by a transversal, then each pair of alternate interior angles is congruent
alternate interior angles theorem
if two parallel lines are cut b a transversal then exactly one pair of consecutive interior angles is supplementary
consecutive interior angles theorem
the ratio of the change along the y-axis to the change along the x-axis between any two points on the line
rise over run
slope
describes how a quantity y changes in relation to quantity x
rate of change
two non-vertical lines have the same slope if and only if hey are parallel
all vertical lines are parallel
slopes of parallel lines
two non-vertical lines are perpendicular if and only if the product of their slopes is -1, vertical lines are perpendicular
slopes of perpendicular lines
y=mx+b
where m is the slope of the line and b is the y-intecept
slope-intercept form
y-y1=m(x-x1)
where (x1, y1) is any point on the line and m is the slope of the line
point-slope form
the equation of this term is y=b where b is the y-intercept of the line
horizontal line equation
the equation of this term is x=a where a is the x-intercept of the line
vertical line equation
if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
converse of corresponding angles postulate
if given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line
parallel postulate
if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
alternate exterior angles converse
if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
consecutive interior angles converse
if two lines in a plane are cut by a transversal so that a pair f alternate interior angles is congruent, then the lines are parallel
alternate interior angles converse
in a plane, if two lines are perpendicular to the same line, then they are parallel
perpendicular transversal converse