### 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?

**Possible Answers:**

Yes, a reflection over the x-axis

Yes, translation down

No

Yes, a rotation

**Correct answer:**

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 #38 : Geometry

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

**Possible Answers:**

Yes, translation to the left

No

Yes, rotation

Yes, reflection over the x-axis

**Correct answer:**

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 #39 : Geometry

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

**Possible Answers:**

Yes, rotated

Yes, translation down

No

Yes, reflected over the y-axis

**Correct answer:**

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 #2 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

**Possible Answers:**

No

Yes, translation to the right

Yes, reflection over the y-axis

Yes, rotation

**Correct answer:**

Yes, reflection over the y-axis

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 #3 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

**Possible Answers:**

Yes, rotation

No

Yes, reflection over the x-axis

Yes, translation to the left

**Correct answer:**

Yes, translation to the left

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

**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

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 #4 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

**Possible Answers:**

Yes, translation down and to the left

Yes, rotation

Yes, refection over the x-axis

No

**Correct answer:**

No

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 #5 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

**Possible Answers:**

Yes, translation up and to the left

Yes, refection over the y-axis

No

Yes, rotation

**Correct answer:**

No

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 #6 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

**Possible Answers:**

Yes, translation to the left

Yes, refection over the y-axis

Yes, rotation

No

**Correct answer:**

No

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 #7 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

**Possible Answers:**

Yes, refection over the x-axis

Yes, translation down

No

Yes, rotation

**Correct answer:**

No

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.