Acute Angle

an angle less than 90 degrees but more than 0 degrees

Alternate Exterior Angles

Angles that lie outside a pair of lines and on opposite sides of a transversal.

Alternate Exterior Angles Converse

if two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel

Alternate Interior Angles Converse

if two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel

Alternate Interior Angles Theorem

if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Angle

A point and 2 line segments

Angle Addition Postulate

if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC

Angle Bisection

Occurs when a ray bisects an angle

Angle of rotation

angle formed by rays drawn from the center of rotation to a point and its image

Area

the number of square units needed to cover a flat surface

Base Angles Theorem

if two sides of a triangle are congruent, then the angles opposite them are congruent

Between

The space between two points

Bisect

To cut into 2 equal pieces

Collinear (points)

points that lie on the same line

Compass

drafting instrument used for drawing circles

Complementary Angles

two angles whose sum is a right angle/90 degrees

Congruent

Having the same measure

Congruent Complements Theorem

if two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent

Congruent Supplements Theorem

if two angles are supplementary to the same angle (or to congruent angles) then they are congruent

Conjecture

reasoning that involves the formation of conclusions from incomplete evidence

Construction

drawing a figure satisfying certain conditions as part of solving a problem or proving a theorem

Legs of a right triangle

the sides that make up the 90 degree angle of a right triangle

Consecutive Interior Angles

angles that are on the same side of the transversal and inside the two lines

Consecutive Interior Angles Converse

if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

Coordinate

a number that identifies a position relative to an axis

Coplanar

lying in the same plane

Counterexample

an example that shows a conjecture is false

Definition

clarity of outline

Direction of a vector

Determined by the angle that the vector makes with a horizontal line.

Distance

the property created by the space between two objects or points

Distance Formula

d = √[( x₂ - x₁) + (y₂ - y₁)]

Endpoints

points on the ends of line segments

Equiangular

all angles are congruent

Hypotenuse

the side of a right triangle opposite the right angle

Inductive Reasoning

reasoning from detailed facts to general principles

Image

a copy of a Preimage by a translation, rotation, ect...

Initial Point of a Ray

The endpoint on a ray

Integers

-3, -2, -1, 0, 1, 2, 3

Intersection

A point where two or more Lines, line segments, ect cross each other

Isosceles Triangle

A triangle with two congruent sides

Legs of an Angle

are the two congruent sides in a isosceles triangle

Legs of a Right Triangle

in a right triangle the sides that form the right angle are called legs of the right triangle. the side opposite the right angle is the hypotenuse of the triangle

Length

the linear extent in space from one end to the other

Linear Angle

Angle that is exactly 180 degrees

Linear Pair

Two adjacent angles that form a straight line

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Line

A line with no endpoint

Line Segment

part of a line with two endpoints

Magnitude of a vector

AB is the distance from the initial point A to the terminal point B, and is written |AB|

Measure of an Angle

number of degrees in an angle

Midpoint

a point that divides a segment into two congruent segments

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

Natural Numbers

each positive whole number

Ruler

measuring stick consisting of a strip of wood or metal or plastic with a straight edge that is used for drawing straight lines and measuring lengths

Opposite Rays

2 rays that have the same endpoint and go in opposite directions forming a line

Perpendicular Transversal

if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Plane

(mathematics) an unbounded two-dimensional shape

Point

Specific coordinate on a line, line segment, plane, ect...

Postulates

rules that are accepted without proof

Preimage

The original figure in a transformation.

Protractor

drafting instrument used to draw or measure angles

Ray

(mathematics) a straight line extending from a point

Rigid

fixed and unmoving

Segment Bisector

a segment, ray, line, or plane that intersects a segment at its midpoint

Sides of an Angle

the rays that form the angle

Straightedge

hand tool consisting of a flat rigid rectangular bar (metal or wood) that can be used to draw straight lines (or test their straightness)

Undefined Term

A basic figure that is not defined in terms of other figures. The undefined terms in Geometry are point, line, and plane.

Vertex

the point of intersection of lines or the point opposite the base of a figure

Right Angle

the 90 degree angle between two perpendicular lines

Obtuse Angle

an angle between 90 and 180 degrees

Perimeter

The distance around a figure

Straight Angle

An angle that is exactly 180 degrees

Real Numbers

Every number

Relection

The translation of a figure in which the object flips

Reflex Angle

an angle greater than 180 degrees (but less than 360)

Remote Interior Angles Theorem

the exterior angles of a triangle euquals the sum of the 2 remote interior angles.

Right Triangle

a triangle with one right angle

Right Angle Congruence Theorem

all right angles are congruent

Rotation

(mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin

Scalene Triangle

a triangle with no two sides of equal length

Sides of an Angle

the rays that form the angle

Supplementary Angles

Two angles whose sum is 180 degrees

Translation

(mathematics) a transformation in which the origin of the coordinate system is moved to another position but the direction of each axis remains the same

Triangle Sum Theorem

The sum of the measures of the angles of a triangle is 180.

vector

a straight line segment whose length is magnitude and whose orientation in space is direction

Verticle Angle

formed by 2 intersecting like and are opposites of each other which means angles are congruent

Verticle Angle Theorem

verticle angles are congruent

Whole Numbers

0 and the natural numbers