Chapter 1 Foundations of geometry

undefined terms

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

point

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

line

An undefined term in geometry, a line is a strait path that has no thickness and extents forever.

plane

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

collinear

points that lie own the same line

coplanar

points that lie in the same plane

segment

is the part of a line consisting of two points and all points between them

endpoint

is a point at one end of the segment or the starting point of a ray

ray

a part of a line that starts at an endpoint and extends forever in one direction

opposite rays

two rays that have a common endpoint and form a line

postulate

a statement that is accepted as true without proof

coordinate

a pair of numbers used to determine the position of a point on a graph

distance

the amount of space between two points

length

the distance between two points

congruent segments

segments that have the same length

construction

A way of creating a figure that is more precise.

between

a point that lies on the same line but is not one of the end segments

midpoint

a point that divides a segment into two congruent segments

bisects

dividing in half at the midpoint

segment bisector

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

angle

two rays with a common endpoint

vertex

The common endpoint of an angle

interior of an angle

The set of all points between the sides of an angle.

exterior of an angle

the set of all points outside an angle.

measure

how much there is of something that you can quantify

degree

A unit for measuring angles

acute angle

90>angle

right angle

90=angle

obtuse angle

90<angle

strait angle

180=angle

congruent angles

angles of the same degree

angle bisector

a ray that divides an angle into two congruent angles

adjacent angles

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

linear pair

two adjacent angles whose noncommon sides are opposite rays

complementary angles

two angles whose sum is a right angle

supplementary angles

Two angles whose sum is 180 degrees

vertical angles

a pair of opposite congruent angles formed by intersecting lines

perimeter

the size of something as given by the distance around it

area

the measure of space within a boundary

base

a flat bottom on which something is intended to sit

height

how tall something is

diameter

the distance across a circle through its center

radius

a straight line from the center to the perimeter of a circle (or from the center to the surface of a sphere)

circumference

the distance around a circle

pi

The numerical value of the ratio of the circumference of a circle to its diameter of approximately 3.14159.

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.

leg

the two sides that form the right angle of a right triangle

hypotenuse

the side of a right triangle opposite the right angle

transformation

the change in position, size, or shape of a figure

preimage

the original figure

image

figure that results for a transformation

reflection

A transformation of a figure that flips the figure across a line.

rotation

the act of rotating as if on an axis

translation

the act of uniform movement