Chapters 1-2 Flashcards
0
Q
A location, it has neither shape nor size
A
Point
1
Q
Terms explained only by using examples and descriptions
A
Undefined terms
2
Q
Made up of points and has no thickness or width
A
Line
3
Q
A flat surface made up of points that extend infinitely in all directions
A
Plane
4
Q
Points that lie on the same line
A
Collinear
5
Q
Points that do not lie on the same line
A
Noncollinear
6
Q
Point that lie in the same plane
A
Coplanar
7
Q
Points that do not lie in the same plane
A
Noncoplanar
8
Q
The set of all points two or more geometric figures have on common
A
Intersection
9
Q
Terms explained by using undefined terms and/ or other defined terms
A
Definitions or defined terms
10
Q
Defined as a boundless 3D set of all points
A
Space
11
Q
can be measured because it has two endpoints
A
line segment
12
Q
for any two real numbers a and b there is a real number n that is between a and b such that a<b
-this also applies to points on a line
A
betweenness of points
13
Q
segments that have the same measure
A
congruent segments
14
Q
methods of creating geometric figures without using geometric tools
A
constructios
15
Q
the length between two points on a segment with the points on as the endpoints
A
distance
16
Q
a number that can not be expressed as a terminating or repeating decimal
A
irrational number
17
Q
the halfway point between the segment and its endpoints
A
midpoint
18
Q
any line, segment, or plane that intersects a segment at its midpoint
A
segment bisector
19
Q
part of a line, has one endpoint and extends indefinitely in one direction
A
ray
20
Q
if you choose a point on a line, that point determines exactly two of these
- since both of these share a common endpoint, they are collinear
A
opposite rays
21
Q
formed by two noncollinear rays that have a common endpoint
A
angle
22
Q
rays are called this in an angle
A
sides
23
Q
common endpoint in an angle
A
verex
24
something inside the angle
interior
25
something outside of the angle
exterior
26
angles are measured in these units
degrees
27
an angle that has the measure of 90 degrees
right angle
28
an angle with a measure hat is smaller than 90 degrees and larer than 0 degrees
acute
29
an angle with a measure of larger than 90 degrees and smaller than 180 degrees
obtuse angle
30
a ray that divides an angle into two congruent angles
angle bisector
31
two angles that lie in the same plane and have a common vertex an common side, but no common interior points
adjacent angles
32
a pair of adjacent angles with noncommon sides that re opposite rays
linear pair
33
two nonadjacent angles formed by two intersecting lines
| -congruent
vertical angles
34
two angles with measures that have a sum of 90 degrees
complementary angles
35
two angles with measures that have a sum of 180 degrees
supplementary angles
36
lines, segments, or rays that form right angles
perpendicular
37
a closed figure formed by a finite number of coplanar segments called sides such that the sides that have a common endpoint are noncollinear and each side intersects exactly two other sides, but only at their enpoints
polygon
38
the vertex of each angle in a polygon
| -polygons are named by the letters in the vertices, written in order of consecutive vertices
vertex of the polygon
39
if lines were drawn on a polygon, some of the lines pass through the interior of the polygon
concave polygon
40
if lines were drawn on a polygon, none of the lines pass through the interior of the polygon
convex polygon
41
a polygon with 3 sides
triangle
42
a polygon with 4 sides
quadrilateral
43
a polygon with 5 sides
pentagon
44
a polygon with 6 sides
hexagon
45
a polygon with 7 sides
heptagon
46
a polygon with 8 sides
octagon
47
a polygon with 9 sides
nonagon
48
a polygon with a 10 sides
decagon
49
a polygon with 11 sides
hendecaon
50
a polygon with 12 sides
dodecagon
51
a polygon with n sides
n-gon
52
a polygon in which all sides are conruent
equilateral polygon
53
a polygon in which all angles are congruent
equiangular polygon
54
a convex polygon that is both equiangular and equilateral
regular polygon
55
a polygon that is not regular
irreglar polygon
56
the sum of the lengths of the sides of the polygon
perimeter
57
the distance around a circle
circumferece
58
the number of square units needed to over a surface for a figure
area
59
a solid with all flat surfaces that enclose a single region of space
polyhedron
60
each flat surface of a polygon
face
61
line segments where the faces intersect
edges
62
the point where three or moe edges intersect
vertex
63
a polyhedron with two parallel congruent faces called bases connected by a parallelogram faces
prism
64
two parallel congruent faces
bases
65
a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex
pryramid
66
a solid with congruent parallel circular bases connected by a curved surface
cylinder
67
a solid with a circular base connected by a curved surface to a singe vertex
cone
68
a set of points in space that are the same distance from a given point
-has no edges, faces, or vertices
sphere
69
a polyhedron is called this if al of its faces are regular congruent polygons and all of the edges are congruet
regular polyhedron
70
the five types of regular polyhedrons
Platonic Solids
71
a 2D measurement of the surface of a solid figure
surface are
72
the measure of the amount of space enclosed by a solid figure
volume
73
reasoning that uses a number of specific examples to arrive at a conclusion
inductive reasoning
74
a concluding statement reached using inductive reasoning
conjecture
75
a false example to show that a conjecture is not true
counterexample
76
a sentence that is either true or false
statement
77
tells if a statement is either true or false
truth value
78
has the opposite meaning as well as an opposte truth value of a statement
negation
79
two or more statements joined by the work and or or form this
compound statement
80
a compound statement using the word and is called this
| -true only when both statements that form it are true
conjunction
81
a compound statement that uses the word or is called this
disjunction
82
a statement that can be written in if-then form
conditional statement
83
Ex: if p then q
if-then statement
84
the phrase immediately following the word if in a conditional statement
hypothesis
85
the phrase immediately following the word then in a conditional statement
conclusion
86
other statements that are based on a given conditional statement
related conditionals
87
this is formed by exchanging the hypothesis and conclusion of the conditional
converse
88
this is formed by negating both the hypothesis and conclusion of the conditional
inverse
89
this is formed b negating both the hypothesis and the conclusion of the converse of the conditional
contrapositive
90
statements with the same truth values are said to be this
logically equivalent
91
this type of reasoning uses facts, rules, definitions, or properties to reach logical conclusions from given statements
deductive reasoning
92
logically correct method of proving a conjecture
valid
93
one valid form of deductive reasoning is this
Law of Detachment
94
anther valid form of deductive reasoning
-allows you to draw conclusions from two true conditional statements when the conclusion of one statement is the hypothesis of the other
Law of Syllogism
95
a statement that is accepted as true without proof
postulate or axiom
96
once a statement or conjecture has been proven, it is called this ad it can be used as a reason to justify statements in other proofs
theorem
97
you can create this by forming a logical chain of statements liking the given to what you are trying to prove
deductive reasoning
98
one method f proving statements and conjectures
| -involves writing a paragraph to explain why a conjecture for a given situation is true
paragraph proof
99
another name for a paragraph proof
informal proofs
100
a proof that is made up of a series of algebraic statements
algebraic proof
101
contains statements and reasons organized in two columns
two-column proof or formal proof
102
if A, B, and C are collinear, then point Bis between A and C if and only if AB+BC=AC
segment Addition Postulate
103
the points on any line or line segment can be put into one-to-one correspondence with real numbers
Ruler Postulate
104
reflexive property of congruence, symmetric property of congruence, and transitive property of congruence
properties of segment congruence
105
given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 and 180
protractor postulate
106
if two angles form a linear pair, then they are supplementary angles
supplementary theormem
107
if the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles
complementary theorem
108
reflexive property of congruence, symmetric property of congruence, and transitive property of congruence
properties of angle congruence
109
angles supplementary to the same angle or to congruent angles are congruent
congruent supplements theorem
110
angles complementary to the same angle or to congruent angles are congruent
congruent complements theorem
111
if two angles are vertical angles, then they are congruent
vertical angles theorem
112
-perpendicular lines intersect to form 4 right angles; all right angles are congruent; perpendicular lines form congruent adjacent angles; if 2 right angles are congruent and supplementary, then each angle is a right angle; if 2 congruent angles form a linear pair, then they are right angles
right angle theorems
