Answer :
Let's go through each statement step-by-step to determine its truth value.
1. An image created by a reflection will always be congruent to its pre-image.
- A reflection is a type of congruence transformation. This means that the size and shape of the figure do not change; only its position and orientation are altered. Therefore, the image will always be congruent to its pre-image.
- Verdict: True
2. An image and its pre-image are always the same distance from the line of reflection.
- By definition, a reflection creates a mirror image over a line (the line of reflection). For each point on the pre-image, the corresponding point on the image is equidistant from the line of reflection but on the opposite side.
- Verdict: True
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.
- When a point on the pre-image lies exactly on the line of reflection, it doesn't move during the reflection because it is already symmetric about that line.
- Verdict: True
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- The line of reflection acts as the perpendicular bisector of any line segment connecting a point on the pre-image to its corresponding point on the image. Hence, it is perpendicular to those segments.
- Verdict: True
5. The line segments connecting corresponding vertices are all congruent to each other.
- The line segments connecting corresponding points (one from the pre-image and one from the image) are not necessarily congruent to each other. Their lengths depend on how far each point is from the line of reflection.
- Verdict: False
6. The line segments connecting corresponding vertices are all parallel to each other.
- Since the reflection line can be in different orientations, the line segments between corresponding points may not be parallel. These line segments are perpendicular to the reflection line but not necessarily parallel to each other.
- Verdict: False
Based on the above analysis, the true statements about reflections 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.
- The line of reflection is perpendicular to the line segments connecting corresponding vertices.
In summary, the true statements are:
1, 2, 3, and 4.
1. An image created by a reflection will always be congruent to its pre-image.
- A reflection is a type of congruence transformation. This means that the size and shape of the figure do not change; only its position and orientation are altered. Therefore, the image will always be congruent to its pre-image.
- Verdict: True
2. An image and its pre-image are always the same distance from the line of reflection.
- By definition, a reflection creates a mirror image over a line (the line of reflection). For each point on the pre-image, the corresponding point on the image is equidistant from the line of reflection but on the opposite side.
- Verdict: True
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.
- When a point on the pre-image lies exactly on the line of reflection, it doesn't move during the reflection because it is already symmetric about that line.
- Verdict: True
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- The line of reflection acts as the perpendicular bisector of any line segment connecting a point on the pre-image to its corresponding point on the image. Hence, it is perpendicular to those segments.
- Verdict: True
5. The line segments connecting corresponding vertices are all congruent to each other.
- The line segments connecting corresponding points (one from the pre-image and one from the image) are not necessarily congruent to each other. Their lengths depend on how far each point is from the line of reflection.
- Verdict: False
6. The line segments connecting corresponding vertices are all parallel to each other.
- Since the reflection line can be in different orientations, the line segments between corresponding points may not be parallel. These line segments are perpendicular to the reflection line but not necessarily parallel to each other.
- Verdict: False
Based on the above analysis, the true statements about reflections 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.
- The line of reflection is perpendicular to the line segments connecting corresponding vertices.
In summary, the true statements are:
1, 2, 3, and 4.
