Similarity and Transformation

BY: Yannick Gordon

Similarity- Two figures are similar if the second can be obtained from the first by a sequence of transformations, and the angles are still same.  You have to use ~ to show if 2 image's angles are similar.  A figure can still be similar if the figure or shape goes through all transformations.

Transformations- Occur when a figure goes through translation, dilation, rotation and reflection.  

TRANSLATION

Translation is when you move a figure up, down, right, or left without changing the figures shape, size, or look .

DILATION

Dilation is when you multiply an image to make it smaller or larger.

ROTATION

Rotation is baisically when you turn an image to the left or right 90, 180, and 270 degreese.

Reflection

Reflection is basically flipping the image to the right, left, up, or down.  Mathematically this term is flipping the image over the x or y-axis.

To find out if two figures or shapes are similar you have see if the has gone through any of the transformations, and if it has then the figures are similar or congruent, but if not then the figures are not similar.  And the figure can be similar if all four steps happen.  Four instance if you have a square and you rotate it 90 degrees,  then translate it 4 units up and 2 units left, then dilate it by 2, and then reflect it over the y-axis the figure will still be similar to preimage.

This image shows how the two images are similar.  See how at the bottom it says angle DEF~angle GHI, that shows that even though the image has gone through dilation the angles are still the same.  That is called a statement.  To identify similarity there doesn't have to be all three angles it can just be two or one.

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