points, lines and planes

POINTS, LINES AND POINTS, LINES AND PLANESPLANES

OBJECTIVESOBJECTIVESSWBAT:SWBAT:1.1.To understand basic terms To understand basic terms of geometry.of geometry.2.2.To understand and apply To understand and apply basic postulates of geometry.basic postulates of geometry.

What is Geometry?What is Geometry? Geometry is the visual study of shapes, sizes, patterns,

and positions. It occurred in all cultures, through at least one of these five strands of human activities:

1. building/structures 2. motion 3. navigating 4. art/patterns 5. measurement

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.

LINELINEA A LINELINE is a series of points that extends is a series of points that extends

in 2 opposite directions without end.in 2 opposite directions without end.

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 has no is a flat surface that has no

thickness and goes on forever in all thickness and goes on forever in all directions.directions.

Imagine sitting on an island in the middle of Imagine sitting on an island in the middle of the ocean. No matter which way you look…the ocean. No matter which way you look…all you see is water…forever.all you see 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 RT or LINE ST or LINE RSLINE RS

R

TS

RTRS

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

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 ..

.

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

A A postulatepostulate or or axiomaxiom is an is an accepted statement of fact.accepted statement of fact.

Postulate 1-1Postulate 1-1

Through any two points there is exactly Through any two points there is exactly one line. one line.

Postulate 1-2Postulate 1-2

If two lines intersect, then they intersect in If two lines intersect, then they intersect in exactly one point.exactly one point.

AA

BB

XX

Postulate 1-3Postulate 1-3

If two planes intersect, then they intersect in exactly one If two planes intersect, then they intersect in exactly one point.point.

Postulate 1-4Postulate 1-4

Through any three noncollinear points there is exactly Through any three noncollinear points there is exactly one plane. one plane.