Geometry Vocab

Inductive reasoning

The process of reasoning that a rule or statement is true because specific cases are true

Conjecture

A statement that is believed to be true

Expression

A mathematical phrase that contains operations, numbers, and/or variables

Constant

A value that does not change

Difference

The result of subtraction

Function rule

An algebraic expression that defines a function

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

Variable

A symbol used to represent a quantity that can change

Coefficient

A number multiplied by a variable

Formula

A literal equation that states a rule for a relationship among quantities

Equation

A mathematical sentence that shows two expressions are equivalent

Segment of a line

A part of a line consisting of two end points and all points between them

Midpoint

The point that divides a segment into two congruent segments

Congruent

Having the same size and shape, denoted by

*objects and shapes use congruent

Equal

Having the same numeric value

*measurements and distances use equal

Bisect

To divide into two congruent parts

Proof

An argument that uses logic to show that a conclusion is true

Postulate

A statement that is accepted as true without proof. Also called an axiom.

Distance

The absolute value of the difference of the coordinates of the points

*a measurement, numeric

Length

The distance between the two endpoints of a segment

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.

Intersect

To have one or more points in common

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.

Hypothesis

The part of a conditional statement following the word if.

Conclusion

The part of a conditional statement following the word then.

Inverse operations

Operations that undo each other

Converse

The statement formed by exchanging the hypothesis and the conclusion of a conditional statement

Contrapositive

The statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement

Truth value

A statement can have a truth value of true or false

Biconditional statement

A statement that can be written in the form “p if and only if q.”

Counterexample

An example that proves that a conjecture or statement is false

Negation

The negation of statement p is “not p,” written as .

Logically equivalent statements

Statements that have the same truth value

Deductive reasoning

The process of using logic to draw conclusions

Law of Syllogism

If a, then b. If b, then c. If a, then c.

a→bb→ca→c

Point

An undefined term in geometry, it names a location and has no size.

Line

An undefined term in geometry , a line is a straight path that has no thickness and extends forever

Plane

An undefined term in geometry, a flat surface that has no thickness and extends forever

Ray

An undefined term in geometry , a part of a line that starts at an endpoint and extends forever in one direction

Undefined term

A basic figure that is not defined in terms of other figures.

*point, line, ray and plane

Endpoint

A point at an end of a segment or the starting point of a ray.

Opposite rays

Two rays that have a common endpoint and form a line

Collinear

Points that lie on the same line

Coplanar

Points that lie in the same plane

Non collinear

Points that do not lie on the same line

Non coplanar

Points that do not lie on the same plane

Vertex

Common point of two rays that form an angle.

measure

Size of an object (an angle or length)

Degrees

What we measure angles in

Side of an Angle

One of two rays that form an angle

Angle addition

The process of adding 2 angle measures

Angle bisector

A ray that divides an angle into two congruent angles

Acute angle

An angle that measures greater than 0 and less than 90 degrees

Right angle

An angle that measures 90 degrees

Obtuse

An angle that measures greater than 90 and less that 180 degrees

Straight Angle

An angle formed by two opposite rays that measures 180 degrees

Adjacent angles

Two angles in the same plane with a common vertex and a common side, but no common interior points

Non adjacent

two angles in the same plane that do not have a common side

Interior of an angle

Between the two rays that form the angle

Exterior of an angle

Outside the two rays that form the angle

On an angle

On one of the 2 rays that form the angle

Protractor

Used to measure angles.

Supplementary angles

Two angles whose measures have a sum of 180 degrees

Complementary angles

Two angles whose measures have a sum of 90 degrees

Linear Pair

A pair of adjacent angles whose noncommon sides are opposite rays

Vertical angles

The non adjacent angles formed by two intersecting lines

Substitution

The process of exchanging two equal values with in a problem

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

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

Angle Addition Postulate

If d is on the interior of / ABC, then / ABD + / DBC = / ABC

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

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

Definition

A statement that describes a mathematical object and can be written as a true biconditional statement.

Defn of Bisector

Use in a proof when concept of bisector is introduced

Defn Straight Angle

Use in a proof when concept of straight angle is introduced

Defn of Congruence

Use in a proof to state that two things are the same size and shape

Defn of Equality

Use in a proof to state that two things are equal in value

Transitive Property of Equality

a = b, and b = c, so a = c