Determine if each transformation does or does not preserve congruence and drag it to the appropriate box.
Does Preserve Congruence Does NOT Preserve Congruence
rotation reflection translation dilation
rotation - Does Preserve Congruence
reflection - Does Preserve Congruence
translation - Does Preserve Congruence
dilation - Does NOT Preserve Congruence
To determine if each transformation preserves congruence, we need to understand what each transformation does.
1. Rotation: A rotation is a transformation that turns a figure around a fixed point called the center of rotation. If the angle of rotation is the same for two figures, the rotation preserves congruence.
2. Reflection: A reflection is a transformation that flips a figure over a line called the line of reflection. If the line of reflection is the same for two figures, the reflection preserves congruence.
3. Translation: A translation is a transformation that slides a figure from one position to another without changing its size, shape, or orientation. Since the translation moves the figure without rotating or flipping it, translation preserves congruence.
4. Dilation: A dilation is a transformation that changes the size of a figure without changing its shape or orientation. A dilation does not preserve congruence because the size of the figure changes.
Now, let's categorize each transformation:
- Rotation: Does Preserve Congruence
- Reflection: Does Preserve Congruence
- Translation: Does Preserve Congruence
- Dilation: Does NOT Preserve Congruence
Please note that dilation does not preserve congruence because the size of the figure changes.
To determine if each transformation preserves congruence, we need to understand what each transformation does:
1. Rotation: A rotation is a transformation that turns a figure around a fixed point called the center of rotation. The figure remains the same shape and size, just in a different position.
If a rotation preserves congruence, it means that the original figure and the rotated figure are congruent.
To determine if a rotation preserves congruence, we need to check if the distance between corresponding points remains the same after the rotation.
2. Reflection: A reflection is a transformation that flips a figure over a mirror line. The figure remains the same shape and size, just flipped.
If a reflection preserves congruence, it means that the original figure and the reflected figure are congruent.
To determine if a reflection preserves congruence, we need to check if the distance between corresponding points remains the same after the reflection.
3. Translation: A translation is a transformation that slides a figure in a particular direction without changing its shape or size.
If a translation preserves congruence, it means that the original figure and the translated figure are congruent.
To determine if a translation preserves congruence, we need to check if the distance between corresponding points remains the same after the translation.
4. Dilation: A dilation is a transformation that changes the size of a figure without changing its shape. It either enlarges or reduces the figure.
If a dilation preserves congruence, it means that the original figure and the dilated figure are congruent.
To determine if a dilation preserves congruence, we need to check if the ratio of corresponding side lengths remains the same after dilation.
Based on these explanations, you can drag each transformation to the appropriate box.