Geometry Unit 1

angle

a figure formed by two rays with a common endpoint

plane

a flat surface that has no thickness and extends forever

euclid

a greek mathematician and teacher who lived in the 3rd century BC

segment bisector

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

point

a location in space that has neither size nor dimension

construction

a method of creating a geometric figure that is mathematically precise by using a compass and straightedge

coordinate

a number that corresponds to a point

coordinate plane

a plane that is divided into four regions by a horizontal line, called the x-axis, and a vertical line, called the y-axis

midpoint

a point that bisects a segment into two congruent segments

line segment

a portion of a line consisting of two points and all the points between them

ray

a portion of a line that starts at one point and extends forever in only one direction

dimension

a property of space consisting of the measure of distance in one direction

angle bisector

a ray that bisects an angle into two congruent angles

postulate

a statement accepted as true without proof as a basis for reasoning; another name for an axiom

line

a straight path that has no thickness and extends forever

axiom

a universally accepted principle which does not require proof

straight angle

an angle whose measure is 180 degrees and whose rays form a straight line

right angle

an angle whose measure is exactly 90 degrees

acute angle

an angle whose measure is greater than 0 degrees and less than 90 degrees

obtuse angle

an angle whose measure is greater than 90 degrees but less than 180 degrees

bisect

dividing into two equal or congruent parts

euclidean geometry

geometry based on the axioms of euclid

solid geometry

geometry that deals with three-dimensional objects

plane geometry

geometry that deals with two-dimensional objects

differential geometry

geometry that uses calculus to study how geometric functions respond to changing variables

congruent

having the same shape and size

congruent segments

line segments that have the same length

quadrant

one of four regions into which a coordinate plane is divided

linear pair of angles

pair of adjacent angles whose noncommon sides are two opposite rays that form a straight line

collinear points

points that lie on the same line

coplanar points

points that lie on the same plane

interior of an angle

the set of points between the two sides of an angle

exterior of an angle

the set of points outside an angle

space

the unlimited region in which all things exist

supplementary angles

two angles in which the sum of their measures equals 180 degrees

complementary angles

two angles in which the sum of their measures equals 90 degrees

adjacent angles

two angles that share a common vertex and one common side but have no common interior points

vertical angles

two nonadjacent angles formed by two intersecting lines

undefined terms

terms used to describe basic geometric figures that are fundamental to all other geometric figures and, as such, cannot be defined by using other geometric terms

geometry

the branch of mathematics that deals with the study of geometric figures, such as points, lines, planes, and solids, and the deduction of properties, measurements, and relationships of those figures

vertex

the common endpoint of the rays of an angle

endpoint

the point at either end of a line segment or the point at the start of a ray

origin

the point where the x-axis and the y-axis intersect on a coordinate plane

ordered pair

the set of coordinates that indicates the position of a point on a coordinate plane