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Biconditional
p if and only if q," single statement that is equivalent to writing the conditional statement and its converse
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Conclusion
The part of the conditional statement that follows the word "then." (Notation is q)
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Conditional Statement
Has the form "If p, then q." p is the hypothesis and q is the conclusion
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Conjecture
A conclusion reached by inductive reasoning
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Contrapositive
Formed by interchanging and negating the hypothesis and conclusion "If not q, then not p"
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Converse
Formed by interchanging the hypothesis and conclusion "If q, then p"
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Counterexample
An example of a conditional statement in which the hypothesis is fulfilled and the conclusion is not fulfilled. Proves that the statement is false
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Deductive Reasoning
Using the laws of logic to prove statements (theorems) from known statements (postulates and previously proved theorems)
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Equivalent Statements
Having the same truth value
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Hypothesis
In a conditional statement, it comes after "if"...the p in "if p, then q."
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Inductive Reasoning
Making a conjecture about several examples after looking for a pattern in the examples
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Intuitive Reasoning
Using your feelings
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Inverse
Negating the hypothesis and conclusion "If not p, then not q"
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Law of Detachment
If "If p, then q" is a true conditional statement and p is true, then q is true
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Law of Syllogism
If "If p, then q" and "If q, then r" are true conditional statements, then "If p, then r" is also true
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Negation
The denial of a statement "Not p"
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Truth Value
naming a statement true or false
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Transformation
Movement of a pre-image using reflection translation rotation or dilation
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Reflection
Isometric flip motion
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Rotation
Isometric turn motion
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Translation
Isometric slide motion
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Dilation
A similarity transformation that has a center and scale factor, can be an enlargement or a reduction
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Pre-image
Original object before a transformation
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Image
The object after a transformation
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Congruent
Same size and shape
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Isometry
Congruent transformation
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Angle of Rotation
The angle at which a figure is rotated
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Center of Dilation
Point about which a dilation is performed
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Center of Rotation
Fixed point around which a rotation occurs
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Equidistant
Same or equal distance
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Line of Reflection
For every point on a figure, there is a reflection image of that point over this line
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Prime Notation
Symbolic representation given to images as a result of a transformation
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Similarity Transformation
Dilation
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Symmetry
A figure has this if there is an isometry that maps the figure onto itself
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Corresponding
Matching parts of two or more figures
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Mapping
A one-to-one correspondence between points of two figures
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Scale Factor
The number that describes the size change from an original figure to its
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Composition of Motions
Two or more motions done in sequence
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Matrix
A collection of data using rows and columns
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Dimensions of Matrix
Row by Column
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Identity Matrix
Matrix when used results in the original matrix e11 = 1 e12 = 0 e21 =0 e22 = 1
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Acute Angle
An angle x whose measure is 0 < x< 90
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Adjacent Angles
A pair of angles that: 1)Share a common vertex
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Analytic Geometry
Coordinate based geometry
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Angle Bisector
A ray, line, or plane that divides an angle into two congruent angles
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Bisect
Divided into two equal or congruent parts
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Collinear
On the same line
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Complementary Angles
A pair of angles whose sum is 90 degrees
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Congruent Angles
Angles that have the same measure
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Congruent Segments
Segments that have the same length
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Coplanar
On the same plane
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Degree
Unit of measure for an angle (1/360th of a full rotation)
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Dihedral Angle
Angle formed by the intersection of two planes
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Endpoint
Point at the beginning or end of a ray or segment
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Euclidean Geometry
Non-coordinate geometry
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Exterior Point
A point not in the interior or on
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Geometry (overall)
The mathematics of the properties measurement and relationships of points lines angles surfaces and solids
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Infinite
Having no limits or boundaries in time or space or extent or magnitude
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Interior Point
A point not in the exterior or on
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Intersection
Set of points shared by two or more figures
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Line
Infinite set of collinear points
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Linear Pair
A pair of adjacent angles whose non-adjacent sides form opposite rays
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Midpoint
A point that divides a segment into two congruent segments
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Non-collinear
Not on the same line
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Obtuse Angle
An angle q whose measure is 90 < q < 180
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Opposite Rays
Two rays that share a common endpoint and extend in opposite directions
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Parallel Lines
Coplanar lines that never intersect
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Parallel Planes
Two or more planes that never intersect
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Perpendicular Bisector
A segment bisector that intersects the midpoint at right angle
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Perpendicular Lines
Two lines that intersect to form one right angle
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Plane
A boundless flat surface
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Plane Geometry
Branch of geometry that deals with geometric figures which require a plane but not any space for their existence
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Point
Undefined, but can be described as an exact unique sizeless location in space
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Postulate
A statement that requires no proof
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Ray
Has an endpoint and extends infinitely in 1 direction
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Right Angle
An angle q whose measure is q = 90
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Segment
An infinite set of collinear points with finite length
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Segment Bisector
A line, segment, ray, or plane that intersects a midpoint of a segment
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Skew Lines
Non-coplanar lines that never intersect
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Solid Geometry
Branch of geometry that deals with figures which occupy space
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Space
Infinite set of all points everywhere
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Straight Angle
An angle q whose measure is q = 180
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Supplementary Angles
A pair of angles whose sum is 180
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Theorem
A statement that requires proof
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Three-Dimensional Figure
A geometric figure that takes up space in solid geometry like a pyramid or sphere
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Trisect
Divide into three equal or congruent parts
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Two-Dimensional Figure
A geometric figure that takes up no space and can be represented in a plane like a triangle or circle
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Vertex
The shared endpoint of two rays that form an angle
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Vertical Angles
A pair of angles whose sides form opposite rays
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Alternate Exterior Angles
Angles that lie outside two lines on opposite sides of the transversal
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Alternate Interior Angles
Angles that lie between two lines on opposite sides of the transversal
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Consecutive Interior Angles (Same-Side Interior)
Two angles that lie between two lines on the same side of the transversal
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Corresponding Angles
Angles that occupy corresponding positions
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Point-Slope Form - (y - y1) = m(x - x1)
...
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Transversal
A line that intersects two or more coplanar lines at different points
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Slope
(y2 - y1)/(x2 - x1)
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Standard Form
For linear equations, the form Ax + By = C, where A,B,C are integers and A doesn't equal 0
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Slope-Intercept Form
A linear equation of the form y = mx + b
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