Geometry terms and theorems
Terms
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- foot
- intersection of a line and a plane
- determining a plane (4 ways)
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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)
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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)
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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)
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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)
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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)
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at least one right angle
diagonals congruent
w/o proving parallelogram 1st, if all 4 angles right angles - kite (2 ways)
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defn: 2 disjoint pairs of consec. sides of a quadrilateral are congruent
one diagonal is perpendicular bisector of other - rhombus (3 ways)
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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)
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nonparallel sides of zoid congruent
lower or upper base angles of zoid congruent
diagonals of zoid congruent