# Common Core: 8th Grade Math : Understand Similarity of Two-Dimensional Figures: CCSS.Math.Content.8.G.A.4

## Example Questions

### Example Question #1 : 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 transformation and dilation

Yes, transformation

No

Yes, dilation

Yes, transformation

Explanation:

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 two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation.

### Example Question #2 : 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 transformation and dilation

No

Yes, dilation

Yes, transformation

Explanation:

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 two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation.

### Example Question #3 : 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, dilation

Yes, both a transformation and dilation

No

Yes, transformation

Yes, transformation

Explanation:

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 two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation.

### Example Question #4 : 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, dilation

Yes, both a transformation and dilation

No

Yes, transformation

Explanation:

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 two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation.

### Example Question #5 : 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

Yes, dilation

Yes, transformation

No

Yes, both a transformation and dilation

Explanation:

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. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.

### Example Question #6 : 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

Yes, dilation

Yes, transformation

No

Yes, both a transformation and dilation

Explanation:

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. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.

### Example Question #7 : 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

Yes, dilation

Yes, transformation

No

Yes, both a transformation and dilation

Explanation:

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. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.

### Example Question #8 : 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

Yes, both a transformation and dilation

Explanation:

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. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.

### Example Question #9 : 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, dilation

No

Yes, both a transformation and dilation

No

Explanation:

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 #10 : 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

Yes, dilation

Yes, transformation

No

No

Explanation:

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.