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Points, Lines, and Planes

- The Three Undefined Terms of Geometry

A point is an exact location in space.

You are here.

A true point has no length, no width, and no

height.

In fact, you cannot see a true point.

A point is named by a letter.

Point P

P

Lines are 1-dimensional objects that have only

length. Lines continue forever in both

directions.

Because a line has no width or height, you cannot

see a true line.

A line is defined by 2 points.

A

B

Line AB

A ray has a starting point but no ending point.

A ray of light has a starting point (like the

sun) and continues forever in the same direction.

Of course, if the ray hits an object, the light

could be absorbed or reflected.

MIRROR

A ray is also defined by 2 points.

C

D

Ray CD

A line segment has a starting point and an ending

point. Line segments can be measured.

A line segment also defined by 2 points.

E

F

Line Segment EF

Lines can do various things.

Lines can intersect at a point to form angles.

X

Y

Z

Angles are defined by 3 points.

X

Y

Z

XYZ

These angles can be right angles.

90 ?

These angles can be right angles.

R

RST 90

USR 90

c

S

T

U

USV 90

TSV 90

V

When lines intersect to form right angles, they

are said to be perpendicular.

R

UT

RV

c

S

T

U

V

Lines can intersect to form acute and obtuse

angles.

45? acute

135? obtuse

Lines can also run into each other to form

straight angles.

180 ? is a straight angle

Lines do not always intersect.

Lines can be parallel.

Parallel lines have the same slope or steepness.

Is it possible for lines not to intersect and not

be parallel either?

Believe it or not, this is possible. Lets

consider a 3-dimensional rectangular prism.

These 2 lines are not parallel, but they are not

intersecting either.

These lines are called skew lines.

You might have heard the word skewer the last

time you had a barbecue.

S K E W E R

A skewer raises your dinner off the surface of

the grill. The skewer does not intersect the

grill, and the skewer is not parallel to the

grill.

Lines can be

intersecting

skew

parallel

perpendicular

90º

A plane

is a flat

surface that has

length width

but no height.

You can see a plane only if you view it at a

certain angle.

A true plane goes on forever in all directions.

A true plane goes on forever in all directions.

A true plane goes on forever in all directions.

A true plane goes on forever in all directions.

A true plane goes on forever in all directions.

Planes can

Planes can

intersect.

An X-Wing fighter from Star Wars has wings that

intersect.

Planes can

be perpendicular.

Planes can

be parallel.

A Tie Fighter from Star Wars has wings that are

parallel.

Planes can be

intersecting

parallel

perpendicular

The end.