All Common Core: 8th Grade Math Resources
Example Questions
Example Question #1 : Understand 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?
Yes, a reflection over the x-axis
Yes, a rotation
Yes, translation down
No
Yes, a reflection over the x-axis
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.
For this question, we can tell that the triangles 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 rotated because that rotation would have caused the triangle to have its top point facing left or right, not up and down.
Example Question #1 : Understand 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?
No
Yes, reflection over the x-axis
Yes, rotation
Yes, translation to the left
Yes, rotation
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.
For this question, we can tell that the triangles 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 #2 : Understand 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?
Yes, rotated
Yes, translation down
No
Yes, reflected over the y-axis
Yes, rotated
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.
For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been rotated over 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 #40 : Geometry
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
No
Yes, rotation
Yes, reflection over the y-axis
Yes, translation to the right
Yes, reflection over the y-axis
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.
For this question, we can tell that the triangles 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 rotated because that rotation would have caused the triangle to have its top point facing left or right, not up and down.
Example Question #5 : Understand 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?
No
Yes, reflection over the x-axis
Yes, translation to the left
Yes, rotation
Yes, translation to the left
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.
For this question, we can tell that the triangles 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 rotated because that rotation would have caused the triangle to have its top point facing left or right, not up and down.
Example Question #4 : Understand 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?
No
Yes, reflection over the x-axis
Yes, translation down and to the left
Yes, rotation
Yes, translation down and to the left
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.
For this question, we can tell that the triangles 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 rotated because 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?
Yes, rotation
Yes, refection over the x-axis
Yes, translation down and to the left
No
No
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.
For this question, we can tell that the triangles are not the same size, the red triangle is smaller; thus, the triangles are not congruent.
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?
Yes, refection over the y-axis
Yes, rotation
Yes, translation up and to the left
No
No
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.
For this question, we can tell that the triangles 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?
Yes, refection over the y-axis
No
Yes, translation to the left
Yes, rotation
No
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.
For this question, we can tell that the triangles are not the same size, the red triangle is smaller; thus, the triangles are not congruent.
Example Question #44 : Geometry
Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape?
Yes, translation down
Yes, rotation
Yes, refection over the x-axis
No
No
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.
For this question, we can tell that the triangles are not the same size, the red triangle is narrower; thus, the triangles are not congruent.