# Transformations

## Shape and Size

If you fold a paper and cut out a geometrical figure, you get two different figures but they have the same size and the same shape. You can move the figures, turn them around and place them upside down.Two figures having the same shape and same size are called congruent figures.

There are three things you can do with a geometrical figure without changing its geometrical properties. You can move it, this is called translating it; you can rotate it and you can reflect it, making a mirror image. All these transformations demonstrated in the worksheet above.

## Translation

The red arrow is called a vector. A vector has a direction and a length. If you check the check box you can see that all the vertices of the polygon are translated along the same vector. The gray arrows are all parallel.

You make a vector in GeoGebra by using the tool Vector between Two Points .

You make a translation by using the tool Translate Object by Vector . Click on the object you want to translate and then on the vector. The object itself is not translated but a translated copy of the object is created.

## Reflection

If you check the check box a segment is drawn between each point and its mirror point. Each such segment is perpendicular to the line (the mirror). A point and its mirror point have the same perpendicular distance to the line.

You make a reflection by using the tool Reflect Object in Line . Click on the object and then on the line.

## Rotation

In order to rotate an object you need an angle.

• Make two segments with one common endpoint A. Use the tool Segment between Two points .
• Use the tool Angle . Click on one of the segments, then on the other segment. An angle called α appears (α is the first letter in the Greek alphabet).
• Create a geometrical object, a circle or a polygon.
• Use the tool Rotate Object around Point by Angle . Click on the geometrical object; then on the point A; then on the angle α. You can click either in the drawing pad or in the algebra view.

# further info:

find what geometrical figures are congruent: