Common Core: 8th Grade Math : Understand Congruency of Two-Dimensional Figures: CCSS.Math.Content.8.G.A.2

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

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Example Questions

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Example Question #1 :在20tand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?

1

Possible Answers:

No

Yes, translation down

Yes, arotation

Yes, a reflection over the x-axis

Correct answer:

Yes, a reflection over the x-axis

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are the same size; thus, the triangles are congruent. The red triangle has been flipped; thus, the triangle has been reflected over the x-axis.

The triangle has not undergone a translation, because a translation would have only moved the triangle, not flipped it. Also, the triangle has not been rotatedbecause that rotation would have caused the triangle to have its top point facing left or right, not up and down.

Example Question #31 :Geometry

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


2

Possible Answers:

No

Yes, reflection over the x-axis

Yes, rotation

Yes, translation to the left

Correct answer:

Yes, rotation

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are the same size; thus, the triangles are congruent. The red triangle has been rotated; thus, the triangle has been rotated. The point of the triangle moved from pointing up, to pointing to the left.

The triangle has not undergone a translation, because a translation would have only moved the triangle, not rotated. Also, the triangle has not been reflected over the x-axis because it doesn't flip over the x-axis.

Example Question #3 :在20tand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


1

Possible Answers:

No

Yes, rotated

Yes, translation down

Yes, reflected over the y-axis

Correct answer:

Yes, rotated

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are the same size; thus, the triangles are congruent. The red triangle has been rotatedover the x-axis.

The triangle has not undergone a translation, because a translation would have only moved the triangle, not flipped or rotated it. The red triangle has not been flipped over the y-axis; thus, the triangle has not been reflected over the y-axis.

Example Question #4 :在20tand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?

3

Possible Answers:

是的,在轴反射

Yes, translation to the right

Yes,rotation

No

Correct answer:

是的,在轴反射

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are the same size; thus, the triangles are congruent. The red triangle has been flipped; thus, the triangle has been reflected over the y-axis.

The triangle has not undergone a translation, because a translation described would have only moved the triangle to the right, not to the left. Also, the triangle has not been rotatedbecause that rotation would have caused the triangle to have its top point facing left or right, not up and down.

Example Question #1 :在20tand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


3

Possible Answers:

Yes, reflection over the x-axis

Yes, translation to the left

Yes,rotation

No

Correct answer:

Yes, translation to the left

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are the same size; thus, the triangles are congruent. The red triangle has been moved to the left; thus, the triangle has been translated to the left.

The triangle has not undergone a reflection over the x-axis, because the triangle didn't flip over the x-axis. Also, the triangle has not been rotatedbecause that rotation would have caused the triangle to have its top point facing left or right, not up and down.

Example Question #6 :在20tand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?

4

Possible Answers:

No

Yes,rotation

Yes, translation down and to the left

Yes, reflection over the x-axis

Correct answer:

Yes, translation down and to the left

Explanation:

n order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are the same size; thus, the triangles are congruent. The red triangle has been moved to the left and down; thus, the triangle has been translated to the left and down.

The triangle has not undergone a reflection over the x-axis, because the triangle didn't flip over the x-axis and the point of the triangle would be facing down. Also, the triangle has not been rotatedbecause that rotation would have caused the triangle to have its top point facing left or right, not up and down.

Example Question #41 :Geometry

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


5

Possible Answers:

Yes, translation down and to the left

Yes,rotation

No

Yes, refection over the x-axis

Correct answer:

No

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are not the same size, the red triangle is smaller; thus, the triangles are not congruent.

Example Question #42 :Geometry

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


6

Possible Answers:

No

Yes, translation up and to the left

Yes, refection over the y-axis

Yes,rotation

Correct answer:

No

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are not the same size, the red triangle is smaller; thus, the triangles are not congruent.

Example Question #43 :Geometry

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


7

Possible Answers:

No

Yes,rotation

Yes, translation to the left

Yes, refection over the y-axis

Correct answer:

No

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are not the same size, the red triangle is smaller; thus, the triangles are not congruent.

Example Question #1 :在20tand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?


9

Possible Answers:

Yes,rotation

Yes, refection over the x-axis

No

Yes, translation down

Correct answer:

No

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent.

Also, let's recall the types of transformations:

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.

对于这个问题,我们可以告诉三角形are not the same size, the red triangle is narrower; thus, the triangles are not congruent.

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