Chapter 2 Flashcards
Define postulate 2.2 plane separation postulate
Every line divides any plane containing the line into three disjoint sets: the line and two half-planes
Define postulate 2.1 Line Separation Postulate
Every point divides any line through that point into three disjoint sets: the point and two half lines
Define theorem 2.1 Jordan curve theorem
Any simple closed curve divides a plane into
Define half-line
The set of all points on a line on a given side of a given point of the line
Define ray
The union of a half line and it’s origin. It extends infinitely in one direction from a point.
Define between
In an intervening position, separating
Define half plane
A subset of a plane consisting of all points on a given side of a line in the plane. If points P and Q are in the same half-plane, then so is the segment joining them
Define the edge of a half plane
The line that separates the plane in two half-planes. This line is not part of either half-plane
Define a segment
The set consisting of two points A and B and all points in between
Define opposite half planes
Are two half planes that are separated by a particular line of the plane
Define angle
The union of two distinct rays with a common endpoint
Define sides of an angle
The two rays that form an angle
Define vertex of an angle
The common endpoint (origin) of the two rays
Define interior of an angle
The intersection of two half planes each determined by a side of the angle and containing the other side (except for the vertex)
Define exterior of an angle
The compliment of the union of the angle and its interior
Define triangle
The union of segments that connect three non collinear points
Define closed curve
A curve that begins and ends at the same point
Define simple curve
A curve that does not intersect itself (unless the starting and ending points coincide
Define simple closed curve
A simple curve that is also a closed curve
Define circle
The set of all points that are a given distance from a given point in a given plane
Define center of a circle
The given point in the plane
Define radius of the circle
A segment that connects a point on the circle with the center
Define chord of a circle
A segment having both endpoints on the circle
Define diameter
A chord that passes through the center of the circle
Define arc
A curve that is a subset of the circle
Define interior of a circle
The set of all planar points whose distance from the center of the circle is less than the radius
Define exterior of a circle
The set of all planar points whose distance from the center is greater than the length of the radius
Define region
The union of a simple closed curve and its interior. The curve is the boundary of the region
Define convex
The property that if any two points in the shape have a segment that at any point is in the shape
Define concave
a set that is not convex
Define polygon
A simple closed curve that consists only of segments
Define side of a polygon
One of the segments that define the polygon
Define vertex of a polygon
An endpoint of a side of the polygon
Define angle of a polygon
Is an angle with two properties: it’s vertex is a vertex of the polygon and each side of the angle contains the side of the polygon
Define equilateral polygon
A polygon in which all the side have the same length
Define equiangular polygon
A convex polygon in which all angle have the same degree measure
Define regular polygon
Is a polygon that is both equilateral and equiangular
Define diagonal of a polygon
Any segment that connects two vertices but is not a side of the polygon
Define interior of a convex polygon
The intersection of the interiors of its angle
Define the exterior of a convex polygon
The Union of the exteriors of its angles
Define a surface
A connected set of points in space having only the thickness of a point
Define sphere
A surface in space consisting of the set of all points at a given distance from a given point
Define center of a sphere
The given point
Define radius of a sphere
The segment that connects a point of the sphere with the center
Define closed surface
A surface with a finite size that divides other points in space into an interior and an exterior
Define solid
The union of a closed surface and its interior
Define cone
The union of a region and all segments that connect the boundary of the region with a specific non coplanar point
Define cylinder
The union of two regions of the same size and shape in different parallel planes, and the set of all segments that join corresponding points on the boundaries of the region
When is a cone or cylinder circular?
When each base is a circle
Define prism
A cylinder with polygonal region as bases
Define pyramid
A cone with a polygonal region as its base
Define polyhedron
A closed surface made up of polygonal regions
Define face of a polyhedron
One of the polygonal regions that form the surface of the polyhedron
