Answer :
Sure, let's analyze each statement about reflections.
1. An image created by a reflection will always be congruent to its pre-image.
- This statement is true. Reflections are rigid transformations, meaning they preserve the size and shape of the figure. Therefore, the image after reflection is congruent to the pre-image.
2. An image and its pre-image are always the same distance from the line of reflection.
- This statement is also true. When a figure is reflected over a line, every point and its image are equidistant from the line of reflection.
3. If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image point.
- This statement is true as well. If a point is on the line of reflection, it will not move during the reflection because it is essentially its own mirror image.
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- This statement is true. The line of reflection acts as the perpendicular bisector for the segments connecting each point and its image.
5. The line segments connecting corresponding vertices are all congruent to each other.
- This statement is true. The segments connecting corresponding points (pre-image and image) are of equal length because reflections preserve distance.
6. The line segments connecting corresponding vertices are all parallel to each other.
- This statement is true as well. The segments connecting corresponding vertices are not only equal in length but they are also parallel to each other. This is because these segments are perpendicular to the line of reflection, which maintains their parallel nature.
To summarize, all the given statements about reflections are true. That means the correct answers are:
- An image created by a reflection will always be congruent to its pre-image.
- An image and its pre-image are always the same distance from the line of reflection.
- If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image point.
- The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- The line segments connecting corresponding vertices are all congruent to each other.
- The line segments connecting corresponding vertices are all parallel to each other.
So, the result for the question "Which statements are true about reflections? Check all that apply." is:
[True, True, True, True, True, True]
1. An image created by a reflection will always be congruent to its pre-image.
- This statement is true. Reflections are rigid transformations, meaning they preserve the size and shape of the figure. Therefore, the image after reflection is congruent to the pre-image.
2. An image and its pre-image are always the same distance from the line of reflection.
- This statement is also true. When a figure is reflected over a line, every point and its image are equidistant from the line of reflection.
3. If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image point.
- This statement is true as well. If a point is on the line of reflection, it will not move during the reflection because it is essentially its own mirror image.
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- This statement is true. The line of reflection acts as the perpendicular bisector for the segments connecting each point and its image.
5. The line segments connecting corresponding vertices are all congruent to each other.
- This statement is true. The segments connecting corresponding points (pre-image and image) are of equal length because reflections preserve distance.
6. The line segments connecting corresponding vertices are all parallel to each other.
- This statement is true as well. The segments connecting corresponding vertices are not only equal in length but they are also parallel to each other. This is because these segments are perpendicular to the line of reflection, which maintains their parallel nature.
To summarize, all the given statements about reflections are true. That means the correct answers are:
- An image created by a reflection will always be congruent to its pre-image.
- An image and its pre-image are always the same distance from the line of reflection.
- If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image point.
- The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- The line segments connecting corresponding vertices are all congruent to each other.
- The line segments connecting corresponding vertices are all parallel to each other.
So, the result for the question "Which statements are true about reflections? Check all that apply." is:
[True, True, True, True, True, True]
