Geometry Definitions 3-D figures

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Geometry Definitions 3-D figures
2010-12-07 18:50:09
geometry definitions dimensional

definitons of 3-d figures in geometry
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  1. sphere
    set of points in space a fixed distance (radius) from a certain point (center)
  2. great circle
    points of intersection b/w a plane & the center circle of a sphere
  3. small circle
    any circle on a plan that is not a great circle
  4. conic solid
    given a region (base) & a point (vertex) not in the plane of the region, a conic solid is the set of points b/w the vertex & all points of the base, tog. w/ the vertex & base
  5. cone
    surface of a conic solid whose base is a circle
  6. pyramid
    surface of a conic solid whose base is a polygon
  7. height (altitude) of a pyramid/cone
    distance from the vertex to the nearest point of the base on that surface
  8. Slant height of a pyramid is...(finish sen.; NOT def)
    always shorter than the edge of the lateral surface
  9. Slant height of a lateral surface of a pyramid/cone
    distance from the vertex to the nearest point of the base on that surface
  10. Definition of a plane section of a 3-D figure
    intersection of that figure w/ a plane
  11. elevation
    a view of the front, side, or back of a 3-D figure such as a house or building
  12. plan
    a bird's eye view of a 3-D figure
  13. net
    2-D figure that can be folded into a 3-D figure
  14. Point-Line-Plane Postulate (7 parts)
    • given a line in a plane, there exists a point in the plane not in the line. Given a plane in space there exists a point in space not on the plane
    • every line is a set of points that can be put into a one-to-one correspondence w/ the real #s, w/ any point on it corresponding to 0 & any other point corresponding to 1
    • through any two points, there is exactly one line
    • if two points lie in a plane, the line b/w them lies in the plane
    • on a number line, there is a unique distance b/w two points
    • through 3 non-collinear points (points that are not on the same line), there is exactly one plane.
    • if 2 different planes have a point in common, then their intersection is a line
  15. a line is perpendicular to a plane when... (2)
    • a line (L) is perpendicular to a plane (X) if and only if it is perpendicular to every line in X through their intersection OR
    • if the measureof an angle b/w a line and a plane is 90 degrees it is perpendicular to the plane
  16. Can a line which is not in a plane be perpendicular to a line in the plane? Explain.
    Yes. Every line oblique to a plane forms a right angle w/ exactly one line in the plane.
  17. How many possible intersection points are there of two non-parallel planes? Explain.
    Undefined or indeterminable, the answer is a number that cannot be measured.