## 144 terms · Geometry vocabulary and posulates

### Associative Property of Addition

a property of real numbers that states that the sum or product of a set of numbers is the same, regardless of how the numbers are grouped. (a +b) + c =a+ (b +c)

### Associative Property of Multiplication

a property of real numbers that states that the sum or product of a set of numbers is the same, regardless of how the numbers are grouped. (ab)c =a(bc)

### Betweenness

Given two numbers, another number is said to be between those two numbers if it is greater than the first but less than the second

### Bisector of an Angle

A ray whose endpoint is the vertex of the angle an that divides the angle into two congruents angles

### Bisector of a line Segment

any line, or subset of a line, that interests the segment at its midpoint

### Coordinate

an ordered pair of numbers that identifies a point on a coordinate plane, written as (x,y)

### Distributive Property

a property of real numbers that states that the product of the sum or difference of two numbers is the same as the sum or difference of their products

### Geometry

is a branch of mathematics that defines and relates the basic properties and measurement of the line segments and angles

### half- line/ray

a part of line that consists of a point on the line, called an endpoint, and all the points on one side of the endpoint

### Line segment

a set of points consisteing of two points on a line, called endpoints, and all the points on the line between the endpoints

### Line

An infinite set of points in opposite directions forming a straight path, it has only one dimension, length

### Midpoint

A point of the that line segment that divides the segment into tow congruent segments

### Non- collinear set of points

a set of three of more points that do not all lie on the same straight line

### polygon

a closed figure in a plane that is the union of the line segments such that the segments intersect only at their endpoints and no segments sharing a common endpoint are collinear

### set

a collection of objects such that it is possible to determine whether a given object belong to a collection or not

### vertex

the common endpoint of two sides of a polygon, the common endpoint of two rays that form an angle, the common point where two or more edges of a 3-D solid meet

### Conjecture

Statements that are likely to be true but not yet been proved true by a deductive proof

### Deductive Reasoning

Uses the laws of logic to combine definitions and general statements that we know to be true to reach a valid conclusion

### Direct proof

A proof that starts with the given statements and uses the laws of logic to arrive at the statement to be proved

### Equivalence Relation

A relation for which these postulates (reflective, symmetric and transitive) are true

### Generalization

A proposition asserting something to be true either of all members of a certain class or of an indefinite part of that class

### Indirect proof/Proof by contradiction

A proof that starts with the negation of the statement to be proved and used the laws of logic to show that it is false

### Inductive Reasoning

The method of reasoning in which a series of particular examples leads to a conclusion

### Substitution Postulate

A quantity may be substituted for its equal in any statment of equality

### Subtraction Postulate

If equal quantities are sbutracted from equal quantities, the differences are equal

### Adjactent Angles

Two angles in a plane that share a common side and share a common vertex but have no interior points in common

### ASA Triangle Congruence

Two triangles are congruent if two angles and the included side of one triangle are congruent, respectively, two angles and the included side of the other

### SAS Triangle Congruence

Two triangles are congruent if two sides and the included angle of one triangle are congruent, respectiviely, two sides and teh included angle of the other

### SSS Triangle Congruence

Two triangles are congruent if the three sides of one triangle are congruent respectively to the thtree sides of the other

### Altitude of a Triangle

A line segment (of its length) Drawn from a vertex perpendicular to the line containing the oppostite side

### Circumcenter

The point where the three perependicular biserctors of the sides of a triangle interest

### Geometric Construction

A drawing of geometric figure done using only a pencil, a compass and a straightedge, or their equivalents

### Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite these sides are congruent

### Median of a Triangle

A line segment that joints any vertex of the triangle to the midpoint of the opposite side

### Perpendicular Bisector of a Line Segment

A line, a line segment or a ray that is perpendicular to the line segment at its midpoint

### Axis of Symmetry

The line where the figure could be folded so that parts of the figure on opposite sides of the line would coincide

### Coordinate Plane

A plane spanned by the x axis and y axis in which th ecoordinates of a point are its distances from two interesecting perpendicular axes

### Glide Reflection

A composition of transformations of the plane that consists of a line reflection and a translation in the direction of the line of reflections performed in either order

### Oppostie Isometry

A transformation that preserves distance but changes the order or orientation from clockwise to counterclockwise or form counterclockwise to clockwise

### Transformation

A one-to-one correspondence between two sets of points, S and S^1, such that every point in set S corresponds to one and only one point in the S^1, called its image, and every point in S^1 is the image of one and only one point in S called its preimage

### Translation

A transformation of the plane that moves every point in the plane in the same distance in the same direction

### Additon Postulate of Inequalities

1) If equal quantities are added to unequal quantities, then the sums are unequal in the same order. 2) If unequal quantities are added to unequal quantities, then the sum is unequal in the same order

### Adjacent Interior Angles

The angle that is next to the angle but on the inside of the triangle

### Exterior Angles of a Polygon

an angle that forms a linear pair with one of the interior angles of the polygon

### Remote Interior angles/ Non-Adjacent

Angles that are in the triangle, but are not adjacent to the angle

### Substitution Postulate of Inequalities

A quanity may be substituted for its equal in any statment of inequality

### Subtraction Postulate of Inequalities

If equal quantities are subtracted from unequal quantities, then the differences are unequal in the same order

### Transitive Property of Inequality

If a, b, and c are real numbers such that a>b, and b>c, then a>c

### Triangle Inequality Theorem

The length of one side of a triangle is less than the sum of the length of the other two sides

### Trichotomy Postulate

Given any two quantities, a and b, one and only one of the following is true: a,b or a=b or a>b

### Conjunction

A compound statement formed by combining 2 simple statements using the word "and" (^)

### Disjunction

A compound statement formed by combining 2 simple statements using the word "or" (v)