Congruence and Similarity

Determining

In determining whether or not it is congruent or similar you need to first know:

Dilation- is the image and preimage are the same figure but not necessarily the same size since the figure can either be enlarged or reduced by a scale factor.

Scale factor- it is the number used to multiply the x and y coordinates to dilate and make it bigger or smaller than the original shape.

Rotation- rotating a figure around center of rotation which can be rotated 90, 180, and 270 degrees around the center of rotation keeping its original form.

Reflection- to transfer a image over the x or y axix

Translation- to move a figure around or into one of the 4 quandrants without changing the shape

Image- the shape after a transformation

Preimage- the shape before a transformation

Similar Figures

When determinig if a shape is similar, all transformations can be used meaning that the angles and sides are the same and are factors of each other when divided or multiplied making equivalent ratios. Or even if you do multiple transformations they are still the same. Watch the video below for more information.

Here is a visual of different ways to know if they are similar

Congruent Figures

For understanding whether a shape is congruent or not, it must stay the same in size. Therefore using dilations would not make them congruent but similar. Watch the video for more information.