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12 Cards in this Set
 Front
 Back
foot

intersection of a line and a plane


determining a plane (4 ways)

3 collinear points determine a plane
a line and a point not on the line determine a plane two intersecting lines determine a plane two parallel lines determine a plane 

intersections with planes (2 postulates)

if a line intersects a plane not containing it, then the intersection is exactly one point
if two planes intersect, their intersection is exactly one line 

line perpendicular to plane
(defn & thm) 
a line is perpendicular to a plane if it is perpendicular to every one of the lines in the plan that pass through its foot
if a line is perpendicular to two distinct lines that lie in a plane and that pass through its foot, then it is perpendicular to the plane. 

parallel planes (3 defn, 1 thm)

defn: a line and a plane are parallel if they do not intersect.
defn: two planes are parallel if they do not intersect defn: two lines are skew if they are not coplanar thm: if a plane intersects two parallel planes, the lines of intersection are parallel 

properties relating to parallel lines and planes (5 props)

if two planes are perpendicular to the same line, they are parallel to each other
if a line is perpendicular to one of two parallel planes, it was perpendicular to the other plane as well. if 2 planes are parallel to the same plane, they are parallel to each other. if a plane is perpendicular to one of two parallel lines, it is perpendicular to the other line as well 

proving a parallelogram (5 ways)

definition: both pairs of opposite sides are parallel
both pairs of opposite sides are congruent one pair of opposite sides are both parallel and congruent diagonals bisect each other both pairs of opposite angles are congruent 

proving rectangle (3 ways)

at least one right angle
diagonals congruent w/o proving parallelogram 1st, if all 4 angles right angles 

kite (2 ways)

defn: 2 disjoint pairs of consec. sides of a quadrilateral are congruent
one diagonal is perpendicular bisector of other 

rhombus (3 ways)

pair of consec. sides congruent
either diagonal bisects 2 angles of parallelogram w/o parallelogram, if diagonals perpendicular bisectors of each other 

square (1)

both rectangle and rhombus


isos. zoid (3)

nonparallel sides of zoid congruent
lower or upper base angles of zoid congruent diagonals of zoid congruent 