Studied by 3 peoplethree undefined terms of geometry
point, line, plane
three characteristics of a postulate
consistent, independent, complete
five characteristics of a definition
accurate, concise, understandable, reversible, objective
intersection
the intersection of a and b, A n B, denotes the set containing the common elements of the given sets
union
the union of a and b, A U B, denotes the set combining all of the elements in both given sets
complement
the compliment of C, C', contains all the elements in the universal set that are not in C
point
identifies a location and has no size
line
straight set of points extending infinitely in each direction that has no width or thickness and contains infinitely many points
plane
infinite flat surface made up of points extending infinitely in both directions that has no thickness and contains infinitely many lines/points
postulate
a statement that is accepted as true without proof
theorem
a statement that can be proven (through a proof)
expansion postulate
A line contains at least two points. A plane contains at least three noncollinear points. Space contains at least four noncoplanar points.
line postulate
only two points in space lie on exactly one line
plane postulate
If two points are in a plane, then the line that contains them is also in that plane
Line Intersection Postulate
If two lines intersect, then their intersection is exactly one point
plane intersection postulate
If two planes intersect, then their intersection is exactly one line.
Theorem 1.3.1
A line and a point not on that line are contained in one and only one plane.
Theorem 1.3.2
two intersecting lines are contained in one and only one plane
Theorem 1.3.3
Two parallel lines are contained in one and only one plane.
accurate
states the term being defined and clearly communicates the concept
concise
definition avoids unnecessary wording while being grammatically correct
understandable
the definition uses only words that have been previously defined or are clearly understood without being defined
reversible
the definition identifies the class to which the object belongs and its distinguishing characteristics
objective
the definition avoids using emotional words, figures of speech, and limitations of time and space
Colinear points
points that lie on the same line
noncolinear points
points that do not lie on the same line
concurrent lines
lines whose intersection is a single point
coplaner points
points that lie on the same plane
noncoplaner points
points that do not lie on the same plane
coplaner lines
lines that lie on the same plane
parallel lines
coplanar lines that do not intersect
parallel planes
planes that do not intersect
skew lines
lines that are not coplanar
convex
a set is convex if every segment with end points in the set completely contained in the set
concave
a set is concave if a segment can be drawn whose endpoints are in the set but the segment is not completely contained in the set
curve
a set of continuous points
simple curve
a curve that does not intersect itself
closed curve
a curve that begins and ends at the same point
regular polygon
both equilateral and equiangular
triangle
3 sides
quadrilateral
4 sides
pentagon
5 sides
hexagon
6 sides
heptagon
7 sides
octagon
8 sides
nonagone
9 sides
decagon
10 sides
hendecagon
11 sides
dodecagon
12 sides
n-gon
anything over 12 sides
three undefined terms of geometry
point, line, plane
three characteristics of a postulate
consistent, independent, complete
five characteristics of a definition
accurate, concise, understandable, reversible, objective
intersection
the intersection of a and b, A n B, denotes the set containing the common elements of the given sets
union
the union of a and b, A U B, denotes the set combining all of the elements in both given sets
complement
the compliment of C, C', contains all the elements in the universal set that are not in C
point
identifies a location and has no size
line
straight set of points extending infinitely in each direction that has no width or thickness and contains infinitely many points
plane
infinite flat surface made up of points extending infinitely in both directions that has no thickness and contains infinitely many lines/points
postulate
a statement that is accepted as true without proof
theorem
a statement that can be proven (through a proof)
expansion postulate
A line contains at least two points. A plane contains at least three noncollinear points. Space contains at least four noncoplanar points.
line postulate
only two points in space lie on exactly one line
plane postulate
If two points are in a plane, then the line that contains them is also in that plane
Line Intersection Postulate
If two lines intersect, then their intersection is exactly one point
plane intersection postulate
If two planes intersect, then their intersection is exactly one line.
Theorem 1.3.1
A line and a point not on that line are contained in one and only one plane.
Theorem 1.3.2
two intersecting lines are contained in one and only one plane
Theorem 1.3.3
Two parallel lines are contained in one and only one plane.
accurate
states the term being defined and clearly communicates the concept
concise
definition avoids unnecessary wording while being grammatically correct
understandable
the definition uses only words that have been previously defined or are clearly understood without being defined
reversible
the definition identifies the class to which the object belongs and its distinguishing characteristics
objective
the definition avoids using emotional words, figures of speech, and limitations of time and space
Colinear points
points that lie on the same line
noncolinear points
points that do not lie on the same line
concurrent lines
lines whose intersection is a single point
coplaner points
points that lie on the same plane
noncoplaner points
points that do not lie on the same plane
coplaner lines
lines that lie on the same plane
parallel lines
coplanar lines that do not intersect
parallel planes
planes that do not intersect
skew lines
lines that are not coplanar
convex
a set is convex if every segment with end points in the set completely contained in the set
concave
a set is concave if a segment can be drawn whose endpoints are in the set but the segment is not completely contained in the set
curve
a set of continuous points
simple curve
a curve that does not intersect itself
closed curve
a curve that begins and ends at the same point
regular polygon
both equilateral and equiangular
triangle
3 sides
quadrilateral
4 sides
pentagon
5 sides
hexagon
6 sides
heptagon
7 sides
octagon
8 sides
nonagone
9 sides
decagon
10 sides
hendecagon
11 sides
dodecagon
12 sides
n-gon
anything over 12 sides
Note
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