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Geometry is a branch of mathematics that is used widely in arts.  It is one of the methods that people use to… 

› Represent their environment. › Interpret ideas. › Create designs or constructions.


The Spiral Ramp at the Vatican?  Or the drawing by MC Escher? 


Point –A position on a line or in a plane.  Line Segment– A line that is bound between two points.  Circumference– A closed curve whose points are all an equal distance from a central point.  Polygon–A closed shape formed by line segments. 


A polygon can be regular… › If it has all equal

sides and angles. 

Or irregular… › If the sides and

angles are different.


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Transformations are modifications made on geometric forms that maintain the basic characteristics of the form.


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Variations in the original form, maintaining the basic values through similarity or proportionality.

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Variations in the position, like rotation, reflection, and translation.


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Congruent figures are two figures that are exactly the same

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Similar figures are two figures that have equal angles but their sides are proportional.


In order to create a similar shape, we can use the technique of enlarging. › All points must move the same direction. › All points must move the same distance. › All angles stay the same. › All lines become proportionally larger.


Next to the polygon, make an external point A.  Measure the distance between the point A and the first vertex (point) of the polygon  Draw a line from point A that passes through point N. Draw a new point at double the distance from point A.

A


Draw a small irregular polygon with a ruler like the initial of your name, an animal, a symbol, etc with a minimum of 6 vertices.  Use the necessary steps to make the shape double it’s size. 


Translation is moving a shape.  Every point of the shape must move: 

› The same distance › In the same direction


Next to your polygon, draw a 5 cm long “translation line” to act as a guide.  Use the ruler to draw equal (5 cm) parellel lines from each vertex. Connect the dots. 


Draw a rotation point (R) next to your polygon.  Connect the point R with the first vertex O.  Place the protractor center at the point R and mark the degrees. In this case, 40º.  Measure the distance from the point to the vertex with a ruler and draw a line of the same length through the 40º mark. This is the new vertex O. Repeat.

R


If we augment the number of sides of a regular polygon, it begins to resemble a circumference.

In order to draw a regular polygon, it can be “inscribed” on a circumference.


A polygon is inscribed when all of it’s vertices touch the circumference without crossing it.  INSCRIBED NOT INSCRIBED 


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http://www.mathopenref.com/constinhe xagon.html

3 eso unit 4 isssuu  
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