group 6 project in math - copy

8/8/2019 Group 6 Project in Math - Copy

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ROUP 6


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MODEL


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PointointvIn geometry, topology and related branches ofmathematics a spatial point describes a specific objectwithin a given space that consists of neither volume,

area, length, nor any other higher dimensional analogue.Thus, a point is a 0-dimensional object. Because of theirnature as one of the simplest geometric concepts, theyare often used in one form or another as the

fundamental constituents of geometry, physics, vectorgraphics, and many other fields.vA dot is the simplest representation of a point.

vA single letter is used to name a point


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A

B

CD

EFG

H

M

J

L k

I

S R Q

PON

oints inoints inhehe modelodel

T


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COLLINEAROLLINEARANDND-ON COLLINEARON COLLINEARPOINTSOINTS


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llinear Pointsllinear PointsvPoints lying on the same line are Collinear Points

vPoints that do not lie on the same line arenon- collinear points.

A B C

U,P,T are non-collinear points

-on Collinearon Collinear


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vThree non-collinear points forms a triangle


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ollinear pointsollinear pointsn the modeln the model

B

H

N

C D

J

PO

E

k

QS R

I

M L

FG


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on Collinearon Collinearoints in theoints in theModelodelB, C, HB, C, I

H, C, I

B, H, I

C, D, I

I, D, JJ, I, C

H, I, N

O,N, H

H, I, OI, O, N

I, O, J

J,O,P

P,I,O

G,M,LM,F,L

G,F,M

G, F, L

F,L,K

E,L,KF,E,K

F,E,L

M,S,RL,R,S

M,L,S

M,L,R

L,R,Q

R,Q,K

L,R,K

A, B, DB, G, AA, D, E


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LinesinesvLines are an idealization of objects and

have no width or height at all and areusually considered to be infinitely long.vWhen geometry is used to model thereal world, lines are used to representstraight objects with negligible width and

height.ine Segmentine SegmentvA line segmentis a part of a linethat is bounded by two distinct endpoints and contains every point on the

line between its end points.


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rallel Linesrallel LinesvLines that do not intersect at a certain point.

A B

C D

AB // CD


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llel Lines in the mollel Lines in the moBC // HI

CD // IJ

HI //NOIJ // OP

GF //MLFE // LK

ML //SRLK //

RQ


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BH // CI

CI // DJ

HN // IO

IO // JP

GM // FL

FL // EKMS // LR

LR // KQ


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CI // FL

DJ // EK

JP // KQ

IO // LR

HN // MS

BH // GM


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ntersecting Linesntersecting LinesvLines that intersect at one point

A B

CE

AC intersects DB at point E


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ntersecting Linesntersecting Linesn the modeln the modelvHJ intersects CO at Point I

vMK intersects FR at point L


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kew Lineskew Linesvare lines that do not intersect and thatare on different planes.

A B

C D

EF

G H

vAB and FH are Skew Lines


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ome Skew Linesome Skew Linesn the modeln the modelBC and FL

CI and FE

MS and NO

JP and RQ


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PlanelanevA plane is any flat, two-dimensional surface

vA plane is a set of point which all lie in aflat surface that extends indefinitely in all

direction

vThree non-collinear points determine a planev

vTwo parallel lines determine a planev

vTwo distinct intersecting line determines aplane

o determine a planeo determine a plane


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lanes in the Modellanes in the Modelq

B, A, DqB, A, GqG, A, EqD, A, EqB, N, P, Dq

G, S, Q, EqB, H, C, IqC, I, J, DqG, M, L, FqF, L, E, KqH, N, O, IqI, O, P, JqM, S, R, LqL, R, K, QqB, N, S, DqD, P, Q, EqM, G, B, H

q

J, P, Q, K


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Anglesngles An angle is a figure formed by two rayswith a common end point.

A

GE

vTwo rays extending infinitely in the space are the sides of the angle.

GA and GE are two sides of angle AGE.

vThe common end point of the two sides of the angle is called the

vertex.

Point G is the vertex of angle AGE


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rts of an anglerts of an anglevThe corner point of an angle is

called the vertex

vAnd the two straight sides

are called arms

vThe angle is the amount ofturn between each arm.


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aming an Angleaming an AngleAn angle is named using a number, vertex, or the vertex

and two points in each side of the angle. A

G E

1This angle can be named asv ngle AOB or AOBv ngle O or Ov ngle 1 or 1

If three letters is used, the middle letter is the vertex ofthe angle.

e.g In angle AGE, G is the vertex.

If one letter is used, it is the vertex of the angle.e.g In angle G, G is the vertex

If a number appears at its vertex, then angle AGE or angleO is also named as angle 1


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v ight Angleight Angle v cute Anglecute Angle

v btuse Anglebtuse Angle v eflex Angleeflex Angle

v traighttraight Anglengle

van angle that is lessthan 90

vAn angle that is exactly

90

van angle that is greaterthan 90 but less than 180

van angle that is greaterthan 180

van angle that is 180 exactly

ypes of Anglesypes of Angles


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ngles in the figurengles in the figure

Reflex

Angle

AcuteAngle

Straight

Angle

ObtuseAngle

Right

Angle


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Trianglesrianglescording to the relative length of their sicording to the relative length of their si

EQUILATERALQUILATERAL ISOSCELESSOSCELES SCALENECALENE

A triangle is one of the basic shapesof geometry: a polygon with threecorners or vertices and three sides or

edges which are line segments.

In an equilateraltriangle all sides havethe same length. An

equilateral triangle isalso a regular polygon

with all anglesmeasuring 60.

In an isosceles triangle,

two sides are equal in lengthIn an scalene

triangle, all sides

are not equal.

:Triangles can be classified
http://en.wikipedia.org/wiki/File:Triangle.Equilateral.svghttp://en.wikipedia.org/wiki/File:Triangle.Equilateral.svghttp://en.wikipedia.org/wiki/File:Triangle.Scalene.svghttp://en.wikipedia.org/wiki/File:Triangle.Isosceles.svghttp://en.wikipedia.org/wiki/File:Triangle.Equilateral.svg


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v y internal anglesy internal anglesv IGHT TRIANGLEIGHT TRIANGLE v BLIQUE TRIANGLEBLIQUE TRIANGLE

v CUTE TRIANGLECUTE TRIANGLE v BTUSE TRIANGLEBTUSE TRIANGLE

A right triangle has one of itsinterior angles measuring 90

Triangles that do not have an angle that

measures 90

A triangle that has allinterior angles measuringless than 90

A triangle that has one angle thatmeasures more than 90


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angles in the figureangles in the figureIsoscelesTriangle

andAcuteTriangle

Right

Triangle


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Pyramidyramid

is a structure where the outer surfaces are triangular and converge

at a point. The base of a pyramid can be trilateral, quadrilateral, orany polygon shape, meaning that a pyramid has at least threetriangular surfaces (at least four faces including the base). Thesquare pyramid, with square base and four triangular outer surfaces,is a common version.


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Cubeube

vIn geometry, a cube is a three-dimensional solid objectbounded by six square faces, facets or sides, with threemeeting at each vertex.


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ectangular Prismectangular Prism

vIn a rectangular cuboid, all angles are right angles, and oppositefaces of a cuboid are equal. It is also a right rectangular prism.The term "rectangular or oblong prism" is ambiguous. Also theterm rectangular parallelepipedor orthogonal parallelepiped is used.


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REFERENCEEFERENCEv :// . . / / .http www icoachmath com SiteMap CollinearPoints htmlv

v :// . . / .http www mathsisfun com angles htmlv

v :// . . / / % %http en wikipedia org wiki Plane_ 28geometry 29v

v :// . . / / % %http en wikipedia org wiki Point_ 28geometry 29v

v :// . . / /http en wikipedia org wiki Trianglev

v :// . . / /http en wikipedia org wiki Pyramidv

v


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group 6 project in math - copy

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