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

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