collinear
points that lie on the same line
noncollinear
points that don't lie on the same line
Coplanar
lines that lie on the same plane
Concurrent
lines that intersect
ray
a definite start and no definite ending
angle
a pair of rays that have the same end point
Triangle
A polygon that has 3 sides
Quadrilateral
A polygon that has 4 sides
Pentagon
A polygon that has 5 sides
Octagon
A polygon that has 8 sides
Commutative
a+b=b+a
ab=ba
Associative
(a+b)+c=a+(b+c)
(ab)c=a(bc)
Additive Identity
a+0=a
Additive Inverse
a+(-a)=0
Multiplicative Inverse
a*(1/a)=1
Converse
reversing the hypothesis and conclusion
Conjunction and table
p and q
Disjunction
p or q
Syllogism
a-->b, b-->c, a-->c
Theorem
statement that is proved by reasoning deductively from already accepted statements
Premise
a-->b,b-->c, c-->d
An Indirect Proof
If not d, then e if e, then f and so on, until we come to a contradiction therefore, not d is false, so d is true
Postulate
Axium
Acute Angle
Angle less then 90 degrees
Obtuse Angle
Angle more then 90 degress
Straight Angle
180 degrees
Right Angle
90 degrees
Corollary
A theorem that can be easily proved as a consequence of a definition a postulate or another theorem
Complementary
2 angles that sum to 90
Supplementary
2 angles that sum to 180
Linear Pairs
2 angles that have a common side and whose other sides are opposite rays
Vertical Angles
2 angles such that the sides of one angle are opposite rays to the sides of the other
Perpendicular
Lines that form a right angle
Polygon
A connected set of at least 3 line segments in the same plane such that each segment intersects exactly 2 others one at each endpoint
Congruent Triangles
2 triangles for which there is a correspondence between their vertices such that all their corresponding sides and angles are equal
ASA
When there are 2 triangles and a pair of angles are equal, pair of sides are equal and finally a pair of angles are equal
SAS
When there are 2 triangles and a pair of sides are equal, pair of angles are equal and finally a pair of sides are equal
Scalene
iff has no equal sides
Isosceles
iff 2 of its sides are equal
Equilateral
iff all of the sides are equal
Obtuse
Iff one angle is more than 90 degrees
Right
iff one of the 3 angles are 90 degrees
Acute
iff all 3 angles are acute
Equiangular
all angles are equal, meaning angles are 60 degrees
Three Possibilities Property
a>b, a=b, b>a
Transitive Property
a>b and b>c then a>c
Addition Property
a>b then a+c>a+b
Subtraction Property
a>b then a-c>a-b
Multiplication Property
a>b, c>0 then ac>bc
Division Property
a>b, c>0 then a/c>b/c
Addition Theorem of Inequality
a>b and c>d, a+c>b+d
Whole Greater than Part
a>0, b>0 and a+b=c, then c>a and c>b
Exterior Angle of a Triangle
An exterior angle of a triangle is greater than either remote interior angle
Parallel lines
lines that lie in the same plane and do not intersect
Transversal
A line that intersects 2 or more lines that lie in the same plane in different points
Corresponding Angles
angles on the same side of a transversal on 2 separate lines in the same position
Alternate Interior Angles
angles on opposite sides of the transversal, in the interior region of 2 lines, on 2 different lines
Alternate Exterior Angles
angles on opposite sides of the transversal, in the exterior region of 2 lines, on 2 different lines
Consecutive Interior Angles
angles on the same side of the transversal in the interior region of 2 lines on 2 different lines
Parallelogram
a quadrilateral whose opposite sides are parallel
A Square
a quadrilateral all of whose sides and angles are equal
A Rhombus
a quadrilateral all whose sides are equal
A Trapezoid
a quadrilateral that has exactly one pair of parallel sides
An Isosceles Trapezoid
A trapezoid whose legs are equal
A Midsegment of a Triangle
A line segment that connects the midpoints of 2 of a triangles sides
A Polygonal Region
The Union of a polygon and its interior
AA Similarity
If 2 angles of one triangle are equal to 2 angles of another triangle, then the triangles are similar