Geometry Vocab
description
Transcript of Geometry Vocab
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Geometry Vocab
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Inductive reasoning
The process of reasoning that a rule or statement is true because specific cases are true
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Conjecture
A statement that is believed to be true
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Expression
A mathematical phrase that contains operations, numbers, and/or variables
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Constant
A value that does not change
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Difference
The result of subtraction
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Function rule
An algebraic expression that defines a function
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Rate of change
A ratio that compares the amount of change in the dependent variable to the amount of change in the independent variable
AKA: SLOPE
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Variable
A symbol used to represent a quantity that can change
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Coefficient
A number multiplied by a variable
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Formula
A literal equation that states a rule for a relationship among quantities
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Equation
A mathematical sentence that shows two expressions are equivalent
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Segment of a line
A part of a line consisting of two end points and all points between them
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Midpoint
The point that divides a segment into two congruent segments
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Congruent
Having the same size and shape, denoted by
*objects and shapes use congruent
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Equal
Having the same numeric value
*measurements and distances use equal
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Bisect
To divide into two congruent parts
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Proof
An argument that uses logic to show that a conclusion is true
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Postulate
A statement that is accepted as true without proof. Also called an axiom.
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Distance
The absolute value of the difference of the coordinates of the points
*a measurement, numeric
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Length
The distance between the two endpoints of a segment
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Construction
A method of creating a figure that is considered to be mathematically precise. Figures may be constructed by using a compass and straightedge, geometry software, or paper folding.
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Intersect
To have one or more points in common
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Conditional statement
A statement that can be written in the form “if p, then q,” where p is the hypothesis and q is the conclusion.
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Hypothesis
The part of a conditional statement following the word if.
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Conclusion
The part of a conditional statement following the word then.
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Inverse operations
Operations that undo each other
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Converse
The statement formed by exchanging the hypothesis and the conclusion of a conditional statement
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Contrapositive
The statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement
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Truth value
A statement can have a truth value of true or false
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Biconditional statement
A statement that can be written in the form “p if and only if q.”
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Counterexample
An example that proves that a conjecture or statement is false
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Negation
The negation of statement p is “not p,” written as .
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Logically equivalent statements
Statements that have the same truth value
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Deductive reasoning
The process of using logic to draw conclusions
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Law of Syllogism
If a, then b. If b, then c. If a, then c.
a→bb→ca→c
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Point
An undefined term in geometry, it names a location and has no size.
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Line
An undefined term in geometry , a line is a straight path that has no thickness and extends forever
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Plane
An undefined term in geometry, a flat surface that has no thickness and extends forever
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Ray
An undefined term in geometry , a part of a line that starts at an endpoint and extends forever in one direction
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Undefined term
A basic figure that is not defined in terms of other figures.
*point, line, ray and plane
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Endpoint
A point at an end of a segment or the starting point of a ray.
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Opposite rays
Two rays that have a common endpoint and form a line
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Collinear
Points that lie on the same line
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Coplanar
Points that lie in the same plane
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Non collinear
Points that do not lie on the same line
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Non coplanar
Points that do not lie on the same plane
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Vertex
Common point of two rays that form an angle.
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measure
Size of an object (an angle or length)
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Degrees
What we measure angles in
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Side of an Angle
One of two rays that form an angle
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Angle addition
The process of adding 2 angle measures
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Angle bisector
A ray that divides an angle into two congruent angles
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Acute angle
An angle that measures greater than 0 and less than 90 degrees
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Right angle
An angle that measures 90 degrees
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Obtuse
An angle that measures greater than 90 and less that 180 degrees
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Straight Angle
An angle formed by two opposite rays that measures 180 degrees
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Adjacent angles
Two angles in the same plane with a common vertex and a common side, but no common interior points
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Non adjacent
two angles in the same plane that do not have a common side
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Interior of an angle
Between the two rays that form the angle
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Exterior of an angle
Outside the two rays that form the angle
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On an angle
On one of the 2 rays that form the angle
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Protractor
Used to measure angles.
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Supplementary angles
Two angles whose measures have a sum of 180 degrees
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Complementary angles
Two angles whose measures have a sum of 90 degrees
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Linear Pair
A pair of adjacent angles whose noncommon sides are opposite rays
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Vertical angles
The non adjacent angles formed by two intersecting lines
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Substitution
The process of exchanging two equal values with in a problem
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Addition Property of Equality
For real numbers a, b, and c, if a = b, then a + c = b + c
*add the same value to each side
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Subtraction Property of Equality
If a, b, and c are real numbers and a = b, then a – c = b – c.
*subtract the same thing from each side
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Angle Addition Postulate
If d is on the interior of / ABC, then / ABD + / DBC = / ABC
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Division Property of Equality
For real numbers a, b and c, where c ≠ 0, if a = b, then .
*divide all terms by the same value
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Multiplication Property of Equality
If a, b, and c are real numbers and a = b, then ac = bc
*multiply all terms by the same value
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Definition
A statement that describes a mathematical object and can be written as a true biconditional statement.
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Defn of Bisector
Use in a proof when concept of bisector is introduced
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Defn Straight Angle
Use in a proof when concept of straight angle is introduced
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Defn of Congruence
Use in a proof to state that two things are the same size and shape
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Defn of Equality
Use in a proof to state that two things are equal in value
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Transitive Property of Equality
a = b, and b = c, so a = c