Bju Geometry Chapter 1

Front 1

Elements

Back 1

Objects in a set

Front 2

Set

Back 2

Any collection of objects

Front 3

Set Builder notation

Back 3

Used to state the rule describing the elements in a set

Front 4

Empty Set (Null Set)

Back 4

A set with no elements is called a

Front 5

Equal sets

Back 5

Sets containing the same elements

Front 6

Subset

Back 6

Means that every element in a set is also in another set

Front 7

Proper Subset

Back 7

Means that every element of a set is in another set but not equal to that set

Front 8

Equivalent

Back 8

Sets that demonstrate one to one correspondence

Front 9

Equivalent

Back 9

Sets having the same number of elements

Front 10

F

Back 10

T/F A set can be an element of another set

Front 11

Universal set

Back 11

A set containing all the elements within the context of a problem

Front 12

Union

Back 12

A set combining all the elements of given sets

Front 13

Intersection

Back 13

Set containing only what is in common with both sets

Front 14

Complement

Back 14

Set of all the elements in the universal set that are not in a given set

Front 15

Binary operations

Back 15

Operations that are applied to two sets

Front 16

Unart operations

Back 16

Operations only using one set

Front 17

Disjoint sets

Back 17

Sets with nothing in common

Front 18

Accurate, Understandable, Reversible, Concise, Objective

Back 18

Five characteristics of good definitions

Front 19

Accurate

Back 19

The definition clearly states the term, avoiding ambiguous language

Front 20

Understandable

Back 20

The definition uses words that have been clearly defined or are clearly understood without being defined

Front 21

Reversible

Back 21

Definition identifies the class to which the object belongs to and its defining atteibutes

Front 22

Concise

Back 22

Avoids unnecessary wording while being grammatically correct

Front 23

Objective

Back 23

Avoids emotional words figured of speech and limitations of time and space

Front 24

Point, Line, Plane

Back 24

The three undefined terms that are the basis of Geometry

Front 25

Point

Back 25

A dot or location with no length or thickness a location in space

Front 26

Line

Back 26

A straight set of points extending infinitely in one dimension

Front 27

Plane

Back 27

A flat surface made of points extending infinitely in two dimensions

Front 28

Space

Back 28

The set of all points

Front 29

Collinear points

Back 29

Pints that lie on the same line

Front 30

Concurrent lines

Back 30

Line whose intersection is at a single point

Front 31

Coplanar points

Back 31

Points that lie on the same plane

Front 32

Coplanar lines

Back 32

Line that lie on the same plane

Front 33

Skew lines

Back 33

Lines that are not coplanar

Front 34

Parallel lines

Back 34

Coplanar lines that do not intersect

Front 35

Parallel planes

Back 35

Planes that do not intersect

Front 36

Geometry

Back 36

An orderly systematic body of mathematical knowledge

Front 37

Undefined terms

Back 37

Forms the basis of geometry

Front 38

Postulates

Back 38

Basic relationships that are aimed to be true without proof

Front 39

Postulates

Back 39

Forms the basis for theorems

Front 40

Theorems

Back 40

Statements Shown to be true by a proof

Front 41

Proof

Back 41

Logical progressions of reasoning

Front 42

Consistent

Back 42

A postulate System is ___________ if they do not contradict each other

Front 43

Independent

Back 43

If no other postulates can be deduced it is

Front 44

Complete

Back 44

Forms a sufficient bar for a full description

Front 45

Expansion postulates

Back 45

A line contains at least two points. A plane contains at least three noncollinear points. Space contains at least four non coplanar points

Front 46

Line postulate

Back 46

Any two points in space lie in exactly one line

Front 47

Plane postulate

Back 47

Three noncollinear points lie on exactly one plane

Front 48

Flat plane postulate

Back 48

If two points lie in a plane the the line containing those two pints lies in the same plane

Front 49

Line intersection postulate

Back 49

If two lines intersect then their intersection is exactly one point

Front 50

Plane intersection postulate

Back 50

If two planes intersect then their intersection is exactly one line

Front 51

Half-line

Back 51

A subset of a line consisting of all the points on a given side of a line

Front 52

Angle

Back 52

The union of two distinct rays with a common endpoint

Front 53

Sides

Back 53

The two rays that form the angle

Front 54

Vertex

Back 54

The common endpoint of an angle

Front 55

Line separation postulate

Back 55

Every point on a line divides the line into three disjoint sets: the point and two half lines

Front 56

Ray

Back 56

The union of the half-line and its origin

Front 57

R-P-S

Back 57

Pont P is between R and S

Front 58

Opposite rays

Back 58

Ray PR is and PS are __________ if P is between R and S

Front 59

Segment

Back 59

A ________ consists of two points and all the points between them

Front 60

Plane separation postulate

Back 60

Every line in a plane divides the plane into three disjoint sets, the line and two half planes

Front 61

Half plane

Back 61

A subset of a plane containing all the points on a given side of a line in the plane

Front 62

Edge

Back 62

The line separating the plane into two half planes

Front 63

Opposite half planes

Back 63

Two half planes within a plane separated by a common edge

Front 64

Coordinate

Back 64

Point on a number line is the number that corresponds to that point

Front 65

Length

Back 65

The distance between two endpoints

Front 66

Congruent

Back 66

Segments with equal lengths

Front 67

Degree

Back 67

1/360 of a circle

Front 68

Congruent

Back 68

Angles with equal measure

Front 69

Adjacent Angles

Back 69

Coplanar angles with a common side but no interior points

Front 70

Tessalation

Back 70

A plane with a pattern of one or more geometric shapes.

Front 71

Circle

Back 71

Set of all points that are the same distance from the center

Front 72

Radius

Back 72

A segment to the center to a point on the circle

Front 73

Region

Back 73

The union of a simple closed curve and its interior

Front 74

Segment

Back 74

Each side of the polygon

Front 75

Vertex

Back 75

Each endpoint of the side

Front 76

Polygon

Back 76

A simple closed curve with only segments

Front 77

Equilateral

Back 77

A polygon with all sides having the same length

Front 78

Equiangular

Back 78

A polygon with all angles being the same

Front 79

Regular

Back 79

A polygon that is equilateral and equiangular

Front 80

Chord

Back 80

A _______ of a circle is any segment whose endpoints are on the circle

Front 81

Circular

Back 81

A cylinder or cone is _________ if each base has a circular region

Front 82

Pyramid

Back 82

A cone with a polygonal region is a

Front 83

Prism

Back 83

A cylinder with a polygonal region

Front 84

Base

Back 84

Prisms and pyramids are classified by their

Front 85

Oblique

Back 85

Cone and cylinders that are not right

Front 86

Sides

Back 86

Polyhedrons are classified by their

Front 87

Sketches

Back 87

Freehand pictures

Front 88

Straight edge and compass

Back 88

Construction only uses

Front 89

T

Back 89

T/F Drawings use a variety of tools including rulers

Front 90

Diameter

Back 90

A chord containing the circles center

Front 91

Arc

Back 91

A curve that is the subset of a circle

Front 92

Surface

Back 92

A connected set of points having the thickness of the point

Front 93

Sphere

Back 93

The set of all points equidistant from the center

Front 94

Radius

Back 94

Any segment from the center to a point on the sphere

Front 95

Cone

Back 95

The union of a region and all segments with a vertex

Front 96

Base

Back 96

The region in a plane blinded by a simple closed curve in a cone

Front 97

Lateral surface

Back 97

The line segment connecting the vertex to the curve

Front 98

Cylinder

Back 98

The union of two parallel surfaces the same size and shape and the set of segments connecting the shapes