Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
56 Cards in this Set
 Front
 Back
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 nonstraight 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 noncommon sides (<AOC). p. 139


Linear pair

Two adjacent angles form a linear pair if and only if their noncommon 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 nonstraight 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 onetoone 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.
