Tools of Geometry

Chapter 1 Vocabulary

Mrs. Robinson

Objective

Chapter 1 Vocabulary Tools of Geometry

Essential Questions

How can I use vocabulary in the real world?

Undefined term

The most basic figures in geometry which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

point

has no dimension. It is usually represented by a small dot

line

A straight path that has no thickness and extends forever

two arrowheads to indicate that the line extends without end in two directions.

plane

A flat surface that has no thickness and extends forever

collinear

Points that lie on the same line

K, L, and M are collinear

M

K

L

N

coplanar

Points that lie on the same plane.

Otherwise they are noncoplanar.

Name four coplanar points

A, B, C, D

segment

Or line segment

The part of a line consisting of two points and all points between them.

endpoint

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

ray

Consists of the initial point

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 or axiom

a statement or rules that is accepted as true without proof.

Postulates about points, lines, and planes help describe geometric properties.

Postulate or axiom pg. 14

Postulate or axiom pg. 20

coordinate

The real number that corresponds to a point

See postulate 1-5 on pg. 20

distance

absolute value of the difference of the coordinates.

AB = |a – b| or |b - a|

A

a

B

b

length

The distance between A and B is also called the length of AB, or AB.

AB = |a – b| or |b - a|

A

a

B

b

construction

a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge.

Sketch, draw, and construct a

segment

congruent to MN.

between

all three points must lie on the same line, and

AB + BC = AC.

congruent segments

Segments that have the same length

midpoint pg. 23

A point on a line segment that divides it into two equal parts

The halfway point of a line segment

Midpoint formula

bisect

To divide into two equal parts.

You can bisect lines, angles, and more. The dividing line is called the "bisector"

segment bisector pg.23

A line, ray or segment which cuts another line segment into two equal parts.

angle

consists of two different rays that have the same initial point.

You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

vertex

A point where two or more straight lines meet. A corner.

plural: vertices

interior of an angle

an angle between points that lie on each side of the angle.

exterior of an angle

an angle not on the angle or in its interior.

measure

the absolute value of the difference of the real numbers paired

degree

A measure for angles. There are 360 degrees in a full rotation.

The symbol for degrees is °

Example: 90 degrees (90°) is a right angle.

acute angle

An angle less than 90° (90° is called a Right Angle)

right angle

An angle which is equal to 90°, one quarter of a full revolution

obtuse angle

An obtuse angle is one which is more than 90° but less than 180°

In other words, it is between a right angle and a straight angle.

straight angle

A straight angle changes the direction to point the opposite way. It looks like a straight line.

It measures 180° (half a revolution, or two right angles)

Types of Angles pg. 30

congruent angle

angles that have the same measure.

The Angle Addition Postulate is very similar to the Segment Addition Postulate

angle bisector

A line that splits an angle into two equal angles. 

("Bisect" means to divide into two equal parts.)

adjacent angles

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

linear pair

Two adjacent angles whose noncommon sides are opposite rays.

The angles of a linear pair form a straight angle

complementary angles

Two angles are if the sum of their measures is 90°

supplementary angles

Two angles are if the sum of their measures is 180°

vertical angles

Two angles are if their sides form two pairs of opposite rays.

perimeter

P of a plane figure is the sum of the side lengths of the figure.

Measured in single units

area

A of a plane figure is the number of non-overlapping square units of a given size that exactly cover the figure.

Measured in square units

Perimeter & Area

base

The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle.

height

The vertical distance from top to bottom

diameter

a segment that passes through the center of the circle and whose endpoints are on a circle.

radius

a segment whose endpoints are the center of the circle and a point on the circle.

circumference

Distance around a circle.

Measured in single units

pi

3.14159265359 …………………..

The ratio of a circle’s circumference to its diameter is the same for all circles. This ratio is represented by the Greek letter (pi). The value of is irrational. Pi is often approximated as 3.14 or .

Circumference and Area of a Circle

The circumference C of a circle is given by the formula or

The area A of a circle is given by the formula

coordinate plane

a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) .

The location, or coordinates, of a point are given by an ordered pair (x, y).

leg

In a right triangle, the two sides that form the right angle

hypotenuse

The side across from the right angle that stretches from one leg to the other

In other words, the longest side of a triangle.

transformation

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

preimage

The original figure

image

The resulting figure

Example of preimage & image

reflection

Or flip

A transformation across a line, called the line of reflection.

Each point and its image are the same distance from the line of reflection

rotation

Or turn

A transformation about a point P, called the center of rotation.

Each point and its image are the same distance from P

translation

Or slide

A transformation in which all the points of a figure move the same distanced in the same direction.