1 1 points, lines and planes
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Transcript of 1 1 points, lines and planes
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 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