All Common Core: 8th Grade Math Resources
Example Questions
Example Question #11 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4
Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation?
Yes, both a transformation and dilation
No
Yes, transformation
Yes, dilation
No
In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation.
Let's recall our key terms:
Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape.
Transformation: A transformation can be described in three ways:
- Rotation: A rotation means turning an image, shape, line, etc. around a central point.
- Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
- Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar.
Example Question #12 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4
Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation?
Yes, transformation
Yes, both a transformation and dilation
No
Yes, dilation
No
In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation.
Let's recall our key terms:
Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape.
Transformation: A transformation can be described in three ways:
- Rotation: A rotation means turning an image, shape, line, etc. around a central point.
- Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
- Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar.