Geometry Chapter 2

Front 1

The set of all points on a line on a given side of a given point of the line.
-Does NOT include its origin!

Back 1

Half-Line

Front 2

Every point divides a line through that point into three disjoint sets: the point and 2 half-lines.

Back 2

Line Separation Postulate

Front 3

The union of a half-line and its origin. It extends infinitely in one direction from a point.

Back 3

Ray

Front 4

B is between A and C if ray BC intersect ray BA is point B when A,B, and C are collinear. A-B-C

Back 4

Between

Front 5

ray BA and ray BC are opposite rays if and only if B is between A and C.

Back 5

Opposite Rays

Front 6

The set of two points A and B and all the points in between.

Back 6

Segment

Front 7

A directed line segment.

Back 7

Vector

Front 8

The 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.)

Back 8

Half-Plane

Front 9

The line that separates the plane into two half-planes (not part of either plane).

Back 9

Edge of a Half-Plane

Front 10

The two half-planes that are separated by a particular line of the plane.

Back 10

Opposite Half-Planes

Front 11

Every line divides any plane containing the line into three disjoint sets: the line and two half-planes.

Back 11

Plane Separation Postulate

Front 12

The union of two distinct rays with a common endpoint.

Back 12

Angle

Front 13

The intersection of the two half-planes each determined by a side angle and containing the other side (except the vertex).

Back 13

Interior of an Angle

Front 14

The compliment of the union of the angle and its interior.

Back 14

Exterior of an Angle

Front 15

The two rays that form the angle.

Back 15

Sides of an Angle

Front 16

The common endpoint (origin) of the two rays.

Back 16

Vertex of an Angle

Front 17

The union of three segments that connect three noncollinear points.

Back 17

Triangle

Front 18

A continuous set of points.

Back 18

Curve

Front 19

A curve that begins and ends at the same point.

Back 19

Closed Curve

Front 20

A curve that does not intersect itself (unless the starting and ending points coincide).

Back 20

Simple Curve

Front 21

A simple curve that is also a closed curve. (no crossover endpoints connect).

Back 21

Simple Closed Curve

Front 22

The set of all points that are a given distance from a given point in a given plane (the center).

Back 22

Circle

Front 23

A segment that connects a point on the circle with the center.

Back 23

Radius

Front 24

A segment with both endpoints on the circle.

Back 24

Chord

Front 25

A chord that passes through the center of the circle.

Back 25

Diameter

Front 26

A curve that is a subset of a circle. (a piece of a circle)

Back 26

Arc

Front 27

The set of all planar points whose distance from the center of the circle is less than the length of the radius.

Back 27

Interior of a Circle

Front 28

The set of all planar points whose distance from the center is greater than the length of the radius.

Back 28

Exterior of a Circle

Front 29

Any simple closed curve divides a plane into three disjoint sets: the curve itself, its interior, and its exterior.

Back 29

Jordan Curve Theorem

Front 30

The union of a simple closed curve and its interior. The curve is called the boundary.

Back 30

Region

Front 31

A set such that any two of its points determine a segment contained IN the set. (a segment connecting two points will never go on the exterior)

Back 31

Convex Set

Front 32

A set that is not convex.

Back 32

Concave Set

Front 33

A simple closed curve that consists only of segments. (no intersections or crossovers) (endpoints meet)

Back 33

Polygon

Front 34

3-sided polygon

Back 34

Triangle

Front 35

4-sided polygon

Back 35

Quadrilateral

Front 36

5-sided polygon

Back 36

Pentagon

Front 37

6-sided polygon

Back 37

Hexagon

Front 38

7-sided polygon

Back 38

Heptagon

Front 39

9-sided polygon

Back 39

Nonagon

Front 40

10-sided polygon

Back 40

Decagon

Front 41

11-sided polygon

Back 41

Hendecagon

Front 42

12-sided polygon

Back 42

Dodecagon

Front 43

n-sided polygon

Back 43

n-gon

Front 44

Polygon with sides the same

Back 44

Equilateral Polygon

Front 45

Polygon with angles the same

Back 45

Equiangular Polygon

Front 46

An equilateral and equiangular polygon

Back 46

Regular Polygon

Front 47

Any segment that connects two vertices but is not a side of the polygon

Back 47

Diagonal

Front 48

A connected set of points in space. (think wrapping paper)

Back 48

Surface

Front 49

A surface with a finite size that divides other points in space into an interior and exterior.

Back 49

Closed Surface

Front 50

A surface in space consisting of the set of all points at a given distance from a given point.

Back 50

Sphere

Front 51

The union of a closed surface and its interior.

Back 51

Solid

Front 52

Union of a region and all segments that connect the boundary of a region with a specific noncoplanar point.

Back 52

Cone

Front 53

Cones with a circle for its base. (ice cream cone)

Back 53

Circular Cone

Front 54

A cone with a polygonal region as its base.

Back 54

Pyramid

Front 55

A cone/pyramid is right if the vertex is centered above the base.

Back 55

Right

Front 56

A cone/pyramid is oblique if it is not right. (vertex is NOT centered above the base)

Back 56

Oblique

Front 57

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 regions.

Back 57

Cylinder

Front 58

8-sided polygon

Back 58

Octagon

Front 59

A cylinder with circles for its bases

Back 59

Circular Cylinder

Front 60

A cylinder with polygonal regions as bases. (straight, flat edges)

Back 60

Prism

Front 61

Closed surface made up of polygonal regions.

Back 61

Polyhedron

Front 62

One of the polygonal regions that form the surface of the polyhedron.

Back 62

Faces

Front 63

Intersection of adjacent faces.

Back 63

Edges

Front 64

A polyhedron that has NO holes.

Back 64

Simple Polyhedra

Front 65

A convex polyhedron where all faces are identical AND the same number of edges meet at each vertex.

Back 65

Regular Polyhedron

Front 66

4-sided polyhedron

Back 66

Tetrahedron

Front 67

5-sided polyhedron

Back 67

Pentahedron

Front 68

6-sided polyhedron

Back 68

Hexahedron

Front 69

7-sided polyhedron

Back 69

Heptahedron

Front 70

8-sided polyhedron

Back 70

Octahedron

Front 71

10-sided polyhedron

Back 71

Decahedron

Front 72

12-sided polyhedron

Back 72

Dodecahedron

Front 73

20-sided polyhedron

Back 73

Icosahedron