geometry introductory terms. point an undefined term. a point has no length or width, it just...

Geometry Introductory Terms

Point An undefined term. A point has

no length or width, it just determines a specific location.

Labels – a single capital letter, can be written out as you see below.- Point A- A

Line An undefined term. Usually defined

as an unlimited collection of points in a straight row. A line extends forever in opposite directions.

AB lineHG

< >h

Labels- Two letters with

two points from the line, any order and double arrow above letters

- The word line then two letters with no arrow above line HG

- The word line with lower case italics letter from the end of the line line h

AB

Ray A figure that begins at a certain point and extends

forever in one direction only. The point where the ray begins is known as its endpoint. Order is very important when labeling a ray. Endpoint must come first then directional point.

AB

HG Can also be written as the word ray then two letters contained on the ray. Endpoint must still come first.

Segment Part or section of a line. It has two end

points with a straight connection. Order is not important when labeling a segment.

PN

CD

Can also be written with the word segment and then the two endpoints from the segment. Order will not be important.

Collinear

Points that lie on the same line. Points P, Q, and R are collinear.

Non-Collinear

Points that do not lie on the same line. H is non-collinear with points A, B, and C.

Plane An undefined term. A flat surface that

extends infinitely in all directions. Three non-collinear points can also determine a plane. Order of the letters to label is not important.

R

Labels:-the word plane with three random letters from the figure (plane ABD)-Just three capital letters mushed together (DCB)- the word plane with a single italic letter from the corner of the figure (plane R)

CoPlanar Elements that lie on the same plane.

This includes points, segments, rays and lines.

Points A, B, and C are coplanar points.

D is not.

Line AC is coplanar with ray BC. Ray AD

is not.

Non-CoPlanar Elements that do not lie on the same

plane. This can be lines, segments, rays or points.

D is non-coplanar with plane ABC. All four points are not contained on the same

plane.

Intersection When lines, rays, segments or planes

meet, they share something in common. This is called an intersection of elements. The intersection can be a point, ray, segment, or line.

Point o

f Int

erse

ction

Perpendicular Lines Two lines in the same plane that

intersect to form 90° angles.

Parallel Lines

Two lines in the same plane which never intersect. Figures are the same distance apart at any given set of points. Planes, segments, and rays can also be parallel. Points cannot be parallel.

Skew Lines, rays, or segments that do not lie in the

same plane, do not intersect and are not parallel. Planes and points cannot be skew.

Line AD is skew with

line BC.

Skew example Find a segment

skew to AB

A

EG

D B

C

F

H

Bisector

A point, line, segment, ray or plane that cuts an element into two congruent parts.

Red ray bisects the angle into two smaller

angles of equal value.

Point M bisects segment AB into two smaller but equal segments.

Perpendicular Bisector A segment, line, plane or ray that creates a right

angle through a segment’s midpoint. The segment is the element bisected. Lines cannot be bisected since they have no endpoints neither can points, rays or planes.

Angle

An angle is formed by two rays which begin at the same point or the intersection of two lines, segments or planes.

Name parts of an angle

A C

B

Naming an Angle

Many different names exist for the same angle. For the angle below, PBC, PBW, CBP, and WBA are all names for the same angle. Notice the vertex is always the middle letter.

Name an angle

A C A D

2

B B C

Measure an angle

Use a protractor.

Must label in degrees.

Put pivot (cross hairs) on the vertex.

Line up zero degree with one side of the angle.

Read measurement using other side of the angle.

Acute Angle

An ACUTE ANGLE is an angle whose measure is more than zero but less than 90º.

Right Angle

A RIGHT ANGLE is an angle whose measure is 90º.

Obtuse Angle

A OBTUSE ANGLE is an angle whose measure is more than 90° but less than 180°.

Straight Angle A STRAIGHT ANGLE is an

angle whose measure is 180°. These are opposite rays which makes a line.

Points Interior, Exterior, On Interior = inside the angle Exterior = outside the angle On = part of the sides of the angle or the

vertex

Example KF is a bisector of angle HKI. Angle HKF

is 5x. Angle FKI is 4x + 9. Solve for x.

Example KF is a bisector of angle HKI. Angle HKI is

8s - 6. Angle FKI is 2(s+11). Solve for x.

Adjacent Angle ADJACENT ANGLES are angles in the

same plane, that have a common vertex and a common side, but no common interior points. Nothing overlaps.

Adjacent Example

I lies in the interior of KJH. If HJI=9x and KJI=3x + 6, find x so that KJ JH.

Linear Pair adjacent angles whose non common sides

are opposite rays. These are two angles that are connected

that make a line.

Linear Pair Example

Name a linear pair of angles

from the drawing shown.

CD

B

A

EP

Vertical Angles Two nonadjacent angles formed by two

intersecting lines or segments. Vertical angles will always have the

same measure.

Vertical Angle Example

Find the value of x.

364x

Complementary Angles If the sum of the measures of two angles is 90

degrees, then the angles are COMPLEMENTARY. The angles do not need to be adjacent but they can

be adjacent.

Complementary Example

The measures of BGC and CGD are complementary. If BGC = 16x – 4 and CGD = 2x + 13, find x and CGD.

Supplementary Angles If the sum of the measures of two angles is 180

degrees, then the angles are SUPPLEMENTARY. A linear pair is supplementary but supplementary

angles do not have to be touching.

Supplement Example

The measure of an angle’s supplement is 44 less than the measure of the angle. Find the measure of the angle and its supplement.

Resources

Photos, diagrams, animations and information collected at:

http://www.Kitchens.com http://www.lhup.edu/~dsimanek/3d/illus2.htm http://www.confluence.org/photo.php?visitid=6067&pic=10 http://www.mathleague.com/help/geometry/basicterms.htm http://www.aplusmath.com/cgi-bin/games/geomatho http://www.e-zgeometry.com/geoglossary/ezglossary.htm