martes, 25 de octubre de 2016

TRIANGLES AND QUADRILATERALS

TRIANGLES 

A triangle has three sides and three angles 
The three angles always add to 180°

TYPES OF TRIANGLES


QUADRILATERALS

Quadrilateral just means "four sides" (quad means four, lateral means side). Any four-sided shape is a QuadrilateralBut the sides have to be straight, and it has to be 2-dimensional 
TYPES OF QUADRILATERALS


General Properties 
        • Four sides (edges)
        • Four vertices or vertexes (corners)
        • The interior angles add up to 360 degrees:
Quadrilateral Angles
Try drawing a quadrilateral, and measure the angles. They should add to 360°

Individual Properties 
Check this web to learn more about them: 

viernes, 21 de octubre de 2016

NOTABLE POINTS AND LINES OF THE TRIANGLE

NOTABLE POINTS OF THE TRIANGLE:


CIRCUMCENTER, INCERTER, ORTHOCENTERResultado de imagen de triangle circumcenter incenter


The INCENTER and CIRCUMCENTER of an EQUILATERAL TRIANGLE are in the exact same point.
Resultado de imagen de triangle circumcenter incenter 


Paper folding - the perpendicular bisectors of a triangle

 

  http://www.regentsprep.org/regents/math/geometry/gc3/perpacute.gif


 

Paper folding - the angle bisectors of a triangle

 

http://www.regentsprep.org/regents/math/geometry/gc3/bisectoracute.gif 

 

BISECTORS AND... KITES?

It is time to get started with the compass! We will draw two VERY IMPORTANT constructions, used in technical drawing to construct almost everything, EVEN A KITE!

It is CRUCIAL that you learn how to do them by observing and practising. SO LETS DO IT!:

PERPENDICULAR BISECTOR LINE

Definition:

The perpendicular bisector is a PERPENDICULAR line that DIVIDES a line segment into TWO EQUAL parts. It also makes a right angle with the line segment. Each point on the perpendicular bisector is at the same distance from each of the endpoints of the original line segment.

It is basically a line which cuts a line segment into two equal parts at 90°.


 http://ceemrr.com/Geometry1/ParPerp/paste_image14.gif 
 




ANGLE BISECTOR LINE

Definition: 

It is a line that DIVIDES the angle in TWO EQUAL parts.

http://www.mathopenref.com/images/constructions/constbisectangle/proof.png




PRACTISE: 

USING THE ANGLE BISECTOR LINE TO CONSTRUCT A KITE


viernes, 7 de octubre de 2016

HOW TO DRAW PARALLEL LINES

These are a few videos to give you information about parallel, perpendicular and intersecting lines and how to draw them using the set square rulers. Then feel free to get artistic!!!


How do we use the set square?
You have to handle your set square softly and with accuracy without exercising too much pressure on them, only the needed one to avoid movement.

PARALLEL LINES
  1. The 45 set square hypotenuse (longest side) is placed attached to the line to which we want to draw the parallels (GUIDE).
  2. The 60-30 set square hypotenuse is attached to the 45 set square leg.
  3. Fix the 60-30 set square and move the 45 set square upwards or downwards drawing the desired parallel lines along its hypotenuse.
PERPENDICULAR LINES
If we want to draw perpendicular lines to one direction, we will have to follow the first two steps as stated for parallel lines and then the following ones:
  1. Having fixed the 60-30 set square, the 45 set square is turned until the other leg is attached to the hypotenuse of the 60-30 set square.
  2. Draw the perpendicular line along the hypotenuse of the 45 set square.
Let's review how to draw parallel and perpendicular lines using the triangular set squares.


jueves, 6 de octubre de 2016

miércoles, 5 de octubre de 2016

GEOMETRY, BASIC TERMS

  • Point (punto)                    

      A point is the place where two lines intersect.
      In geometry, a point has no dimension
      We represent a point with a dot.
      We identify this point with a CAPITAL letter.

  • Line (línea)
        A line is made up of infinite points.
        It has not endpoints and continues endlessly on a plane. 
        These lines are named with small letters such r ,s, t...
  • Ray (semirrecta)
      A ray is a "straight" line that begins at a certain point and extends forever in one direction.
      The point where the ray begins is known as its endpoint.
  • Line segment (segmento)
        A line segment is a portion of a "straight" line.
        A line segment does not extend forever, but has two endpoints.


      The point halfway between the endpoints of a line segment is called the midpoint.  A midpoint divides a line segment into two equal segments.


  • Intersection


        The term intersect is used when lines, ray lines or segments share a common point.
        The point they share is called the point of intersection.

And here you can find a video explaining the differences between line, line segment and ray.

martes, 4 de octubre de 2016

THE MAGIC OF GEOMETRY FOR ARTISTS

For those brave students of 3rd ESO that are struggling with all these geometric constructions, and are looking forward to starting with a more artistic approach. Here is a beautiful and fantastic example where nature and geometry blend together: "NATURE BY NUMBERS" (dealing with the Golden Ratio) a 3D animated short film by Cristobel Vila. Enjoy it!



Now lets see a video that is going to help us with our next project: "The Misterious Magic of Geometry for Artists". 




This is a video with examples for your NEXT PROJECT, size DIN-A3, FREE TECHNIQUE:



lunes, 3 de octubre de 2016

WHAT IS THE POINT OF GEOMETRY?

Just a little bit of help for your Geometric Constructions... Making it easy! Do not forget to check these notes and these Worksheets these for extra help  (not mandatory)
Check these links, learn and enjoy with these introductory videos:

1- THE BASICS OF GEOMETRY

2- HOW TO DRAW TRIANGLES

3- HOW TO DRAW CIRCLES

4- HOW TO MAKE A SQUARE FROM A CIRCLE

5- TYPES OF TRIANGLES


POINT - LINE


PARALLEL LINES - CONVERGING LINES - ANGLE - TRIANGLES


ACUTE, RIGHT AND OBTUSE ANGLES - CIRCLE - RADIUS - CIRCUMFERENCE - DIAMETER


SQUARE - DEGREES


DEGREES IN A TRIANGLE


EQUILATERAL, ISOSCELES AND SCALENE TRIANGLES.
ACUTE, RIGHT ANGLED AND OBTUSE TRIANGLES.



POLYGONS (Wondeful video using Origami Technique)