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56 Cards in this Set
- Front
- Back
Addition property of equality
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If a = b, then a + c = b + c
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Line Intersection Theorem
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Two different lines intersect in at most one point. p.43
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Linear Pair Theorem
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If two angles form a linear pair, then they are supplementary. p.140
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Vertical Angles Theorem:
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If two angles are vertical angles, then they have equal measures. p.141
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Parallel Lines and Slopes Theorem
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Two nonvertical lines are parallel if and only if they have the same slope. p.158
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Transitivity of Parallelism Theorem
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In a plane, if l m and m n, then l n. p. 158
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Two Perpendiculars Theorem
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If two coplanar lines l and m are each perpendicular to the same lines, then they are parallel to each other. p. 162
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Perpendicular to Parallels Theorem1
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In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
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Perpendicular Lines and Slopes Theorem
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Two nonvertical lines are pependicular if and only if the product of their slopes is -1. p.162
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angle
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the union of two rays that have the same endpoint. p. 124
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bisector
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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
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adjacent angles
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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
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Linear pair
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Two adjacent angles form a linear pair if and only if their non-common sides are opposite rays.
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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 |
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parallel lines
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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.
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segment
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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.
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ray
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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.
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opposite rays
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AB and AC are opposite rays if and only if A is between B and C.
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Angle Addition Property
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If VC (except for point V) is in the interior of <AVB, then m<AVC + m<CVB = m<AVB.
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bisector
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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.
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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 |
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vertical angles
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Two non-straight angles are vertical angles if and only if the union of their sides is two lines.
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Reflexive property of equality
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a = a
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Symmetric property of equality
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If a = b, then b = a.
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Transitive Property of Equality
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If a = b and b = c, then a = c.
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Multiplication Property of Equality
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If a = b, then ac = bc.
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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. |
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Parallel lines and slopes theorem
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Two nonvertical lines are parallel if and only if they have the same slope.
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Transitivity of parallelism theorem
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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.
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perpendicular
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Two segments, rays, or lines are perpendicular if and only if the lines containing them form a 90 angle.
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Point Line Postulate:
a. Unique Line Assumption |
Through any two points, there is exactly one line. p.42
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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
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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 |
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Opposite rays
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AB and AC are opposite rays if and only if A is between B and C.
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Distance Postulate:
a. Uniqueness property |
On a line, there is a unique distance between two points.
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Distance Postulate:
b. Distance formula |
If two points on a line have coordinates x and y the distance between them is X - Y .
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Distance Postulate:
c. Additive property- |
If B is on AC, then AB = BC = AC.
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Convex-
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A convex set is a set in which every segment that connects points of the set lies entirely in the set.
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Instance of a conditional-
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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.
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Counterexample to a conditional
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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.
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Converse
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The converse of P q is q P.
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Midpoint-
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The midpoint of a segment AB is the point M on AB with AM = MB.
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Union of two sets-
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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.
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Intersection of two sets
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The intersection of two sets A and B, written A B, is the set of elements which are in both A and B.
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Polygon-
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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.
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Triange Inequality Postulate-
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The sum of the lenghts of any two sides of a triange is greater than the length of the third side.
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vertices- (vertex)
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The endpoints of the sides of a polygon. Singular is vertex.
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Consecutive (or adjacent)-
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Consecutive (or adjacent) sides are sides which share an endpoint. p.96
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Diagonal-
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A diagonal is a segment connecting nonadjacent vertices. p. 96
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equilateral triangle
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all three sides are equal
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isosceles triangle-
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has at least two sides of equal length. p. 97
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scalene triangle-
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a triangle with no sides of the same length. p. 96
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Triangle Inequality Postulate-
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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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. |
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slope
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The slope of the line through
(X1, Y1) and (X2, Y2), with X1 not equal to X2 is Y2 - Y1 X2 - X1 |
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Circle-
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A circle is the set of all points in a plane at a certain distance, its radius, from a certain point, its center.
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