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12 Cards in this Set

  • Front
  • Back
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