If you know what kind of transformation was used to create two figures, you can tell if the figures are congruent or similar. You don't even have to see the two figures to know their relationship! That's because the type of transformation determines how the new figure is related to the original figure.
Use the interactive table below to review what happens in each transformation. See if you can answer the question in the first column before clicking that question to see the answer. Then try to answer the question in the second column before clicking to see the answer in the third column.
| Question | Explanation | Type |
| How does a translation occur? | Each of the points in a figure is moved exactly the same distance to form a new figure. What type of relationship does translation create between two shapes? | Congruence—translation preserves the shape and size of a figure. |
| How does a reflection occur? | A reflection makes a mirror image of a figure by reflecting all the points through a line or a point. What type of relationship does reflection create between two figures? | Congruence—reflection preserves the shape and size of the figure. |
| How does a rotation occur? | A rotation turns a figure around a fixed point. How are the two shapes related when one is used to create a rotation of the other? | The two figures are congruent, since rotation preserves the shape and size of the original figure. |
| How does a dilation occur? | A dilation re-sizes a figure based on some scale factor. The figure can get smaller or it can get bigger. What is the relationship between a dilation and the original figure that was used to create it? | Similarity. Since a dilation preserves the shape but not the size of the figure, two images created by a dilation are not congruent. Instead, they are similar. |
Question
How can you tell if two figures are congruent or similar—without even seeing the figures?
Find out if one of the figures is a transformation of the other. If so, find out what type of transformation was used to create the second figure.
