Sunday 18 November 2018

GEOMETRY

BASIC GEOMETRY CONCEPTS AND DEFINITIONS

GEOMETRY:It is an area which any elements and operations on /in the plane such as points lines or shape.

POINT: It is a point can be defined as the place or location where two lines intersect. A point has not dimensions,no heigh and no width.
       

LINE:A one dimensional object formed of infinites points.It has not endpoints and continues forever in a plane .

RAY: It is a line which begins at a particular point ( called the endpoint) and extends endlessly in one dimension.

MIDPOINT: It´s the point that is halfway between the endpoints of the line segment.

ENDPOINT: It is a point  which a line segment or a ray ends or starts.

LINE SEGMENT: It is a line with two endpoints.

  How calculate de midpoint


LENGTH: It is a measurement of something from end to end.


GEOMETRY DRAWING AND SUPPLIES CONCEPTS AND DEFINITIONS

FREEHAND: Draw by hand without guiding instruments, measurements...

LINE / TECHNICAL DRAWING: It´s  a drawing with the help of supplies. You  used for architecture or enginering plans. 

COMPASS: It´s  a toll for drawing circles and arcs and also for measuring distance between points.


PROTRACTOR: It´s an instrument for measuring or drawing angles. It´s a semicircle graduated in degrees.

SET SQUARES (UK) TRIANGULES (US): There are two special rulers with triangular sape.One is called esquad (45º/90º) and other bevel (60º/30º/90º).

EASER: Use for eliminate the mistakes.

RULER: For making lines.

LINE SEGMENT COPYING: Given the segment AB; copy it  with the same lenght with a compass.

OPERATIONS WITH A SEGMENTS 

ADDITION:


SUBTRACTION:


MULTIPLY:


DIVISION:


LINE BISECTOR: Perpendicular line of a segment through and end point.

PERPENDICULAR LINE TO ANOTHER THROUGH AN OUTER POINT OF IT.

PARALLEL LINE TO ANOTHER ONE THROUGH AN AUTER POINT:

PARALLEL LINE TO A GIVE LINE AT A GIVEN DISTANCE



IMPORTANT DEFINITIONS ABOUT CIRCLES

RADIUS: It´s a length of a line segment from the center to its perimeter (radiuses, plu).

DIAMETER: It´s a line segment that passes through the denter.

CLORD : A line segment which conects two points of the circle NOT THROUGH THE CENTER.

ARC: Segment of a circle.

ARROW: It´s a segment enter chord and arc pass to the center.

CIRCULE: Set of points at the same distance to a point called center.

CIRCONFERENCE: It´s the foll length of a circle.

CENTER: It´s a point equidistant to any points on a circle.

IMPORTANT DEFINITTIONS ABOUT ANGLES AND LINES

PARALLElS: They are two lines which never intersect themselves  all points are EQUIDISTANT.

PERPENDICULAR: They are lines which forming four right angles  90º.

OBLIQUE: They are lines which are not parallels neither perpendicular.

ANGLES: It´s a figure formed by two rays sharing a common endpoint (vertex).

TYPES OF ANGLES (position)

COMPLEMENTARY ANGLES: They are couples of angles which sum (+) is 90º.

SUPLENTARY ANGLES: They are couples of angles which sum is 180º.

TYPES OF ANGLES (form)

1º Form for make an angle.

2º Form for make an angle.

THE ANGLE BISECTOR: When I divide on angle into two equals parts.

OPERATION WITH ANGLES

ADITION:


SUBTRACTION:


MULTIPLY:


DIVIDE: It´s a right angle in three parts equals.

POLYGONS

STAR POLYGONS: It´s a polygon with a star shape created out of linking together non consecutive vertices of a regular polygon.

INSCRIBED POLYGONS: They are polygons place inside circles SA ALL the vertex of the polygon are placed on the circle.

CONVEX POLYGON: Any line draw though the polygon it´s boundary exactly twice.

NON-CONVEX( concave): A line may be found which meets it´s boundary more than twice.


THE TRIANGLES: It´s a flat figure with three sides and three angles.




CONSTRUCTION AN EQUILATERAL TRIANGLE WHEN I KNOW ONE SIDE

                

CONSTRUCTION AN EQUILATERAL TRIANGLE WHEN I KNOW THE RADIUS


   

CONSTRUCTION AN ISOSCELES TRIANGLE WHEN I KNOW 2 SIDES:






MADE A RIGTH TRIANGLE WHEN I KNOW 2 SIDES



DO THE RIGHT TRIANGLE WHEN I KNOW 1 SIDE AND THE APOTHEM 



DO THE TRIANGLE WHEN I KNOW 3 SIDES

QUADRILATERALS:They are polygons with four sides and four angles.

PARALLELOGRAMS:They are cuadrilaterals with two sides of parallel opposite equal sides and two pairs opposite equal angles.



TRAPECIUMS:Only one pair of sides are parallels


DO THE SQUARE WHEN I KNOW A SIDE


CONSTRUCTION OF SQUARE WHEN I KNOW THE RADIUS


DO THE RECTANGLE WHEN I KNOW TWO SIDES 


DO A RECTANGLE WHEN I KNOW A DIAGONAL AND 1 SIDE 


DO THE ROMBUS WHEN I KNOW 2 DIAGONALS 
  

DO THE ROMBOID WHEN I KNOW 1 SIDE AND THE ANGLE  Â





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