We are asked to compare and contrast and figures using a graphic organizer. To do so, we will compare the side measures, angle measures, and used in both similar and congruent figures. First, let's recall what it means for two figures to be similar or congruent.
| Congruent Figures
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Similar Figures
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| Congruent figures have the same shape and size.
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Similar figures have the same shapes, but they can have different sizes.
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Let's compare the side measures of similar and congruent figures.
Side Measures
Since congruent figures have the same size, then the must be equal as well. Similar figures may be different sizes, but one can always be mapped onto the other using a . After a dilation with k, each side of the is k times the length of the corresponding side of the .
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Similar Figures
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Congruent Figures
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| Side Measures
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Proportional
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Equal
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| Angle Measures
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| Transformations Used
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We will compare the angle measures of similar and congruent figures next.
Angle Measures
We know that in congruent figures, are because congruent figures have the same shape.
This means that the measures of corresponding angles are equal in congruent figures. Similar figures also have the same shape, so the corresponding angles of similar figures also have equal measures.
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Similar Figures
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Congruent Figures
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| Side Measures
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Proportional
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Equal
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| Angle Measures
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Equal
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Equal
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| Transformations Used
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Transformations Used
Finally, we will consider which transformations can be used to map one congruent figure onto another and which transformations can be used when the figures are similar. Let's review the transformations we know.
| Translation
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A slides a figure around without turning it. It does not affect the shape or size of the figure.
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| Reflection
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A creates a mirror image of a figure. It does not affect the shape or size of the figure.
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| Rotation
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A turns a figure around a fixed point. It does not affect the shape or size of the figure.
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| Dilation
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A dilation is an enlargement or reduction of the original figure. It does not affect the shape of a figure, but it does change the size.
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Similar figures have the same shape but can have different sizes, so the transformations used must result in figures of the same shape. As we can see, the transformations that do not change the shape of a figure are translations, reflections, rotations, and dilations.
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Similar Figures
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Congruent Figures
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| Side Measures
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Proportional
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Equal
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| Angle Measures
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Equal
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Equal
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| Transformations Used
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Translations, reflections, rotations, and dilations
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Congruent figures also have the same shape but must have the same size as well. This means that we cannot use dilations because the size of the figure would change. The transformations that can be used to map a figure onto a congruent figure are translations, reflections, and rotations.
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Similar Figures
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Congruent Figures
|
| Side Measures
|
Proportional
|
Equal
|
| Angle Measures
|
Equal
|
Equal
|
| Transformations Used
|
Translations, reflections, rotations, and dilations
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Translations, reflections, and rotations
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