POINTS, LINES AND POINTS, LINES AND PLANESPLANES

Jim Smith JCHSJim Smith JCHS

Section 1-1Section 1-1

What is Geometry?What is Geometry?

Geometry is the study of shapesGeometry is the study of shapes They studied Geometry in Ancient They studied Geometry in Ancient

Mesopotamia & Ancient EgyptMesopotamia & Ancient Egypt Geometry is important in the art and Geometry is important in the art and

construction fieldsconstruction fields

POINTPOINT A A POINT POINT is an exact location on is an exact location on

a graph, shape or in space.a graph, shape or in space.

The ball is a The ball is a POINTPOINT on the line. on the line.

LINELINEA A LINELINE goes in opposite directions goes in opposite directions

and never, ever ends.and never, ever ends.

Take a pearl Take a pearl necklacenecklace and stretch it and stretch it out.out.

The pearls are like points on a line.The pearls are like points on a line.

PLANEPLANE A A PLANEPLANE is a flat surface that is a flat surface that

goes on forever in all directions.goes on forever in all directions.

Imagine sitting on an island in the Imagine sitting on an island in the middle of the ocean. No matter middle of the ocean. No matter which way you look…all you see which way you look…all you see is water…forever.is water…forever.

TO NAME A POINT- WE USE TO NAME A POINT- WE USE A CAPTIAL LETTERA CAPTIAL LETTER

.A.A .X.X

TO NAME A LINE- USE ANY 2 TO NAME A LINE- USE ANY 2 POINTS ON THE LINEPOINTS ON THE LINE

LINE RT or LINE ST or LINE RS LINE RT or LINE ST or LINE RS Or a single italicized or cursive Or a single italicized or cursive letterletter..

R

TS

RTRS

p

POINTS ON THE SAME LINE ARE CALLED COLLINEAR POINTS

A, B, AND Y ARE A, B, AND Y ARE COLLINEARCOLLINEAR

AY

B.... ..

TO NAME A PLANE WE USE 3 TO NAME A PLANE WE USE 3 OR 4 OR 4 NONCOLLINEARNONCOLLINEAR POINTS POINTS

PLANE WAG or XAG or WXAPLANE WAG or XAG or WXA

.A.W.

PLANES CAN BE NAMED USING 1 LETTER …. PLANE Q

QX

.G

THE THE INTERSECTIONINTERSECTION OF OF 2 LINES IS A POINT2 LINES IS A POINT

s

S IS THE INTERSECTIONINTERSECTIONOF THE 2 LINES

LINE AB IS CONTAINED IN LINE AB IS CONTAINED IN PLANE PLANE QQ

Q

A B

LINE XY LINE XY INTERSECTSINTERSECTS PLANE PLANE QQ AT POINT XAT POINT X

**Notice that the plane is named withNotice that the plane is named with

a single cursive or italicized lettera single cursive or italicized letter

QX

Y

.

THE ARROW INTERSECTSTHE ARROW INTERSECTS THE TARGET AT 1 POINTTHE TARGET AT 1 POINT

Lines YB and XZ Lines YB and XZ do notdo not intersect intersect

X

YB

ZZ ..

.

These are These are SKEWSKEW. They do not . They do not intersect because they are not in the intersect because they are not in the same plalne!same plalne!

THE INTERSECTION OF 2 THE INTERSECTION OF 2

PLANES IS A PLANES IS A LINELINEA

C

E

F

G

B C

H

D

EE

GG

YY

W. S.P

XX

G.

POINTS AND LINES CONTAINED IN POINTS AND LINES CONTAINED IN THE SAME PLANE ARE CALLED THE SAME PLANE ARE CALLED

COPLANARCOPLANAR