Chapters 1-2 Flashcards
A location, it has neither shape nor size
Point
Terms explained only by using examples and descriptions
Undefined terms
Made up of points and has no thickness or width
Line
A flat surface made up of points that extend infinitely in all directions
Plane
Points that lie on the same line
Collinear
Points that do not lie on the same line
Noncollinear
Point that lie in the same plane
Coplanar
Points that do not lie in the same plane
Noncoplanar
The set of all points two or more geometric figures have on common
Intersection
Terms explained by using undefined terms and/ or other defined terms
Definitions or defined terms
Defined as a boundless 3D set of all points
Space
can be measured because it has two endpoints
line segment
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
betweenness of points
segments that have the same measure
congruent segments
methods of creating geometric figures without using geometric tools
constructios
the length between two points on a segment with the points on as the endpoints
distance
a number that can not be expressed as a terminating or repeating decimal
irrational number
the halfway point between the segment and its endpoints
midpoint
any line, segment, or plane that intersects a segment at its midpoint
segment bisector
part of a line, has one endpoint and extends indefinitely in one direction
ray
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
opposite rays
formed by two noncollinear rays that have a common endpoint
angle
rays are called this in an angle
sides
common endpoint in an angle
verex
something inside the angle
interior
something outside of the angle
exterior
angles are measured in these units
degrees
an angle that has the measure of 90 degrees
right angle
an angle with a measure hat is smaller than 90 degrees and larer than 0 degrees
acute
an angle with a measure of larger than 90 degrees and smaller than 180 degrees
obtuse angle
a ray that divides an angle into two congruent angles
angle bisector
two angles that lie in the same plane and have a common vertex an common side, but no common interior points
adjacent angles
a pair of adjacent angles with noncommon sides that re opposite rays
linear pair
two nonadjacent angles formed by two intersecting lines
-congruent
vertical angles
two angles with measures that have a sum of 90 degrees
complementary angles
two angles with measures that have a sum of 180 degrees
supplementary angles
lines, segments, or rays that form right angles
perpendicular
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
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
if lines were drawn on a polygon, some of the lines pass through the interior of the polygon
concave polygon
if lines were drawn on a polygon, none of the lines pass through the interior of the polygon
convex polygon
a polygon with 3 sides
triangle
a polygon with 4 sides
quadrilateral
a polygon with 5 sides
pentagon
a polygon with 6 sides
hexagon
a polygon with 7 sides
heptagon
a polygon with 8 sides
octagon
a polygon with 9 sides
nonagon
a polygon with a 10 sides
decagon
a polygon with 11 sides
hendecaon
a polygon with 12 sides
dodecagon
a polygon with n sides
n-gon
a polygon in which all sides are conruent
equilateral polygon
a polygon in which all angles are congruent
equiangular polygon
a convex polygon that is both equiangular and equilateral
regular polygon
a polygon that is not regular
irreglar polygon
the sum of the lengths of the sides of the polygon
perimeter
the distance around a circle
circumferece
the number of square units needed to over a surface for a figure
area
a solid with all flat surfaces that enclose a single region of space
polyhedron
each flat surface of a polygon
face
line segments where the faces intersect
edges
the point where three or moe edges intersect
vertex
a polyhedron with two parallel congruent faces called bases connected by a parallelogram faces
prism
two parallel congruent faces
bases
a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex
pryramid
a solid with congruent parallel circular bases connected by a curved surface
cylinder
a solid with a circular base connected by a curved surface to a singe vertex
cone
a set of points in space that are the same distance from a given point
-has no edges, faces, or vertices
sphere
a polyhedron is called this if al of its faces are regular congruent polygons and all of the edges are congruet
regular polyhedron
the five types of regular polyhedrons
Platonic Solids
a 2D measurement of the surface of a solid figure
surface are
the measure of the amount of space enclosed by a solid figure
volume
reasoning that uses a number of specific examples to arrive at a conclusion
inductive reasoning
a concluding statement reached using inductive reasoning
conjecture
a false example to show that a conjecture is not true
counterexample
a sentence that is either true or false
statement
tells if a statement is either true or false
truth value
has the opposite meaning as well as an opposte truth value of a statement
negation
two or more statements joined by the work and or or form this
compound statement
a compound statement using the word and is called this
-true only when both statements that form it are true
conjunction
a compound statement that uses the word or is called this
disjunction
a statement that can be written in if-then form
conditional statement
Ex: if p then q
if-then statement
the phrase immediately following the word if in a conditional statement
hypothesis
the phrase immediately following the word then in a conditional statement
conclusion
other statements that are based on a given conditional statement
related conditionals
this is formed by exchanging the hypothesis and conclusion of the conditional
converse
this is formed by negating both the hypothesis and conclusion of the conditional
inverse
this is formed b negating both the hypothesis and the conclusion of the converse of the conditional
contrapositive
statements with the same truth values are said to be this
logically equivalent
this type of reasoning uses facts, rules, definitions, or properties to reach logical conclusions from given statements
deductive reasoning
logically correct method of proving a conjecture
valid
one valid form of deductive reasoning is this
Law of Detachment
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
a statement that is accepted as true without proof
postulate or axiom
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
you can create this by forming a logical chain of statements liking the given to what you are trying to prove
deductive reasoning
one method f proving statements and conjectures
-involves writing a paragraph to explain why a conjecture for a given situation is true
paragraph proof
another name for a paragraph proof
informal proofs
a proof that is made up of a series of algebraic statements
algebraic proof
contains statements and reasons organized in two columns
two-column proof or formal proof
if A, B, and C are collinear, then point Bis between A and C if and only if AB+BC=AC
segment Addition Postulate
the points on any line or line segment can be put into one-to-one correspondence with real numbers
Ruler Postulate
reflexive property of congruence, symmetric property of congruence, and transitive property of congruence
properties of segment congruence
given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 and 180
protractor postulate
if two angles form a linear pair, then they are supplementary angles
supplementary theormem
if the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles
complementary theorem
reflexive property of congruence, symmetric property of congruence, and transitive property of congruence
properties of angle congruence
angles supplementary to the same angle or to congruent angles are congruent
congruent supplements theorem
angles complementary to the same angle or to congruent angles are congruent
congruent complements theorem
if two angles are vertical angles, then they are congruent
vertical angles theorem
-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
