Chapter 2

Question 0

Define postulate 2.2 plane separation postulate

Answer 0

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

Question 1

Define postulate 2.1 Line Separation Postulate

Answer 1

Every point divides any line through that point into three disjoint sets: the point and two half lines

Question 2

Define theorem 2.1 Jordan curve theorem

Answer 2

Any simple closed curve divides a plane into

Question 4

Define half-line

Answer 4

The set of all points on a line on a given side of a given point of the line

Question 5

Define ray

Answer 5

The union of a half line and it’s origin. It extends infinitely in one direction from a point.

Question 6

Define between

Answer 6

In an intervening position, separating

Question 7

Define half plane

Answer 7

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

Question 8

Define the edge of a half plane

Answer 8

The line that separates the plane in two half-planes. This line is not part of either half-plane

Question 9

Define a segment

Answer 9

The set consisting of two points A and B and all points in between

Question 10

Define opposite half planes

Answer 10

Are two half planes that are separated by a particular line of the plane

Question 11

Define angle

Answer 11

The union of two distinct rays with a common endpoint

Question 12

Define sides of an angle

Answer 12

The two rays that form an angle

Question 13

Define vertex of an angle

Answer 13

The common endpoint (origin) of the two rays

Question 14

Define interior of an angle

Answer 14

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

Question 15

Define exterior of an angle

Answer 15

The compliment of the union of the angle and its interior

Question 16

Define triangle

Answer 16

The union of segments that connect three non collinear points

Question 17

Define closed curve

Answer 17

A curve that begins and ends at the same point

Question 18

Define simple curve

Answer 18

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

Question 19

Define simple closed curve

Answer 19

A simple curve that is also a closed curve

Question 20

Define circle

Answer 20

The set of all points that are a given distance from a given point in a given plane

Question 21

Define center of a circle

Answer 21

The given point in the plane

Question 22

Define radius of the circle

Answer 22

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

Question 23

Define chord of a circle

Answer 23

A segment having both endpoints on the circle

Question 24

Define diameter

Answer 24

A chord that passes through the center of the circle

Question 25

Define arc

Answer 25

A curve that is a subset of the circle

Question 26

Define interior of a circle

Answer 26

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

Question 26

Define exterior of a circle

Answer 26

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

Question 27

Define region

Answer 27

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

Question 28

Define convex

Answer 28

The property that if any two points in the shape have a segment that at any point is in the shape

Question 29

Define concave

Answer 29

a set that is not convex

Question 30

Define polygon

Answer 30

A simple closed curve that consists only of segments

Question 31

Define side of a polygon

Answer 31

One of the segments that define the polygon

Question 32

Define vertex of a polygon

Answer 32

An endpoint of a side of the polygon

Question 33

Define angle of a polygon

Answer 33

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

Question 34

Define equilateral polygon

Answer 34

A polygon in which all the side have the same length

Question 35

Define equiangular polygon

Answer 35

A convex polygon in which all angle have the same degree measure

Question 36

Define regular polygon

Answer 36

Is a polygon that is both equilateral and equiangular

Question 37

Define diagonal of a polygon

Answer 37

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

Question 38

Define interior of a convex polygon

Answer 38

The intersection of the interiors of its angle

Question 39

Define the exterior of a convex polygon

Answer 39

The Union of the exteriors of its angles

Question 40

Define a surface

Answer 40

A connected set of points in space having only the thickness of a point

Question 41

Define sphere

Answer 41

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

Question 42

Define center of a sphere

Answer 42

The given point

Question 43

Define radius of a sphere

Answer 43

The segment that connects a point of the sphere with the center

Question 44

Define closed surface

Answer 44

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

Question 45

Define solid

Answer 45

The union of a closed surface and its interior

Question 46

Define cone

Answer 46

The union of a region and all segments that connect the boundary of the region with a specific non coplanar point

Question 47

Define cylinder

Answer 47

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

Question 48

When is a cone or cylinder circular?

Answer 48

When each base is a circle

Question 49

Define prism

Answer 49

A cylinder with polygonal region as bases

Question 50

Define pyramid

Answer 50

A cone with a polygonal region as its base

Question 51

Define polyhedron

Answer 51

A closed surface made up of polygonal regions

Question 52

Define face of a polyhedron

Answer 52

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