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

Study concepts, example questions & explanations for Common Core: 8th Grade Math

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1

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? 


2

Possible Answers:

Yes, dilation 

Yes, both transformation and dilation 

No

Yes, transformation 

Correct answer:

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? 

1

Possible Answers:

No

Yes, transformation

Yes, dilation 

Yes, both transformation and dilation 

Correct answer:

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? 

3

Possible Answers:

Yes, transformation

Yes, dilation 

No

Yes, both a transformation and dilation 

Correct answer:

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? 


4

Possible Answers:

Yes, both a transformation and dilation 

No

Yes, transformation

Yes, dilation 

Correct answer:

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? 


5

Possible Answers:

Yes, dilation 

No

Yes, both a transformation and dilation 

Yes, transformation

Correct answer:

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? 


6

Possible Answers:

Yes, transformation

No

Yes, dilation

Yes, both a transformation and dilation 

Correct answer:

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? 


7

Possible Answers:

Yes, transformation

No

Yes, dilation 

Yes, both a transformation and dilation 

Correct answer:

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? 

8

Possible Answers:

Yes, both a transformation and dilation 

Yes, dilation 

No

Yes, transformation

Correct answer:

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? 


9

Possible Answers:

No

Yes, transformation

Yes, dilation 

Yes, both a transformation and dilation

Correct answer:

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? 

10

Possible Answers:

Yes, dilation 

No

Yes, transformation

Yes, both a transformation and dilation 

Correct answer:

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. 

 

← Previous 1
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: