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56 Cards in this Set

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Addition property of equality
If a = b, then a + c = b + c
Line Intersection Theorem
Two different lines intersect in at most one point. p.43
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary. p.140
Vertical Angles Theorem:
If two angles are vertical angles, then they have equal measures. p.141
Parallel Lines and Slopes Theorem
Two nonvertical lines are parallel if and only if they have the same slope. p.158
Transitivity of Parallelism Theorem
In a plane, if l m and m n, then l n. p. 158
Two Perpendiculars Theorem
If two coplanar lines l and m are each perpendicular to the same lines, then they are parallel to each other. p. 162
Perpendicular to Parallels Theorem1
In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
Perpendicular Lines and Slopes Theorem
Two nonvertical lines are pependicular if and only if the product of their slopes is -1. p.162
angle
the union of two rays that have the same endpoint. p. 124
bisector
VR is the bisector of <PVQ if and only if VR (except for point V) is in the interior of <PVQ and m<PVR = m<PVQ. p. 127
adjacent angles
Two non-straight and non zero angles are adjacent angles if and only if a common side (OB in the figure) is interior to the angle formed by the non-common sides (<AOC). p. 139
Linear pair
Two adjacent angles form a linear pair if and only if their non-common sides are opposite rays.
Complimentary
Supplementary
If the measures of two angles are m1 and m2, then the angles are
a. complementary if and only if m1 + m2 = 90.
b. supplementary if and only if m1 + m2 = 180
parallel lines
two coplanar lines m and n are parallel lines, written m n, if and only if they have no points in common or they are identical.
segment
The segment (or line segment) with endpoints A and B, denoted AB, is the set consisting of the distinct points A and B and all points between A and B.
ray
The ray with endpoint A and containing a second point B, denoted AB consists of the points on AB and all points for which B is between each of them and A.
opposite rays
AB and AC are opposite rays if and only if A is between B and C.
Angle Addition Property
If VC (except for point V) is in the interior of <AVB, then m<AVC + m<CVB = m<AVB.
bisector
VR is the bisector of <PVQ if and only if VR (except for point V) is in the interior of <PVQ and m<PVR = m<RVQ.
Angles:
zero
acute
right
obtuse
straight
zero if m = 0
acute if and only if 0 < m < 90
right if and only if m = 90
obtuse if and only if 90 < m < 180
straight if and only if m = 180
vertical angles
Two non-straight angles are vertical angles if and only if the union of their sides is two lines.
Reflexive property of equality
a = a
Symmetric property of equality
If a = b, then b = a.
Transitive Property of Equality
If a = b and b = c, then a = c.
Multiplication Property of Equality
If a = b, then ac = bc.
Corresponding Angles Postulate


Suppose two coplanar lines are cut by a transversal...
a. If two corresponding angles have the same measure, then the lines are parallel.
b. If the lines are parallel, then corresponding angles have the same measure.
Parallel lines and slopes theorem
Two nonvertical lines are parallel if and only if they have the same slope.
Transitivity of parallelism theorem
In a plane, if line l is parallel to line m and line m is parallel to line n, then line l is parallel to line n.
perpendicular
Two segments, rays, or lines are perpendicular if and only if the lines containing them form a 90 angle.
Point Line Postulate:
a. Unique Line Assumption
Through any two points, there is exactly one line. p.42
Point Line Postulate:
b. Number Line Assumption
Every line is a set of points that can be put into a one-to-one correspondence with the real numbers, with any point corresponding to 0 and any other point corresponding to 1. p.42
Point Line Postulate:
c. Dimension Assumption
1. Given a line in a plane, there is at least one point in the plane that is not on the line.
2. Given a plane in space, there is at least one point in space that is not in the plane. p.42
Opposite rays
AB and AC are opposite rays if and only if A is between B and C.
Distance Postulate:
a. Uniqueness property
On a line, there is a unique distance between two points.
Distance Postulate:
b. Distance formula
If two points on a line have coordinates x and y the distance between them is X - Y .
Distance Postulate:
c. Additive property-
If B is on AC, then AB = BC = AC.
Convex-
A convex set is a set in which every segment that connects points of the set lies entirely in the set.
Instance of a conditional-
An instance of a conditional is a specific case in which both the antecedent (if part) and the consequent (then part) of the conditional are true.
Counterexample to a conditional
A counterexample to a conditional is a specific case for which the antecedent (if part) of the conditional is true and its consequent (then part) is false.
Converse
The converse of P q is q P.
Midpoint-
The midpoint of a segment AB is the point M on AB with AM = MB.
Union of two sets-
The union of two sets A and B, written A B, is the set of elements which are in A, in B, or in both A and B.
Intersection of two sets
The intersection of two sets A and B, written A B, is the set of elements which are in both A and B.
Polygon-
A polygon is the union of segments in the same plane such that each segment intersects exactly two others, one at each of its endpoints.
Triange Inequality Postulate-
The sum of the lenghts of any two sides of a triange is greater than the length of the third side.
vertices- (vertex)
The endpoints of the sides of a polygon. Singular is vertex.
Consecutive (or adjacent)-
Consecutive (or adjacent) sides are sides which share an endpoint. p.96
Diagonal-
A diagonal is a segment connecting nonadjacent vertices. p. 96
equilateral triangle
all three sides are equal
isosceles triangle-
has at least two sides of equal length. p. 97
scalene triangle-
a triangle with no sides of the same length. p. 96
Triangle Inequality Postulate-
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Postulates of Inequality and Operations:
Transitive
Addition
Multiplication
Transitive-
If a<b and b<c, then a<c.
Addition-
If a<b, then a+c<b+c.
Multiplication-
If a < b and c > 0, then ac < bc.
If a < b and c < 0, then ac > bc.
slope
The slope of the line through
(X1, Y1) and (X2, Y2),
with X1 not equal to X2 is

Y2 - Y1

X2 - X1
Circle-
A circle is the set of all points in a plane at a certain distance, its radius, from a certain point, its center.