Answer :
When it comes to reflections in geometry, certain properties hold true. Here are the detailed explanations of which statements about reflections are true:
1. An image created by a reflection will always be congruent to its pre-image.
- This statement is true. In reflections, the shape and size of the image do not change, only its orientation does. Therefore, the image remains 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 true. By definition, a reflection in a line ensures that each 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.
- This statement is true. Any point that lies on the line of reflection does not move during the reflection. Hence, the point remains the same.
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- This statement is true. The line of reflection acts as a perpendicular bisector to the line segments that join corresponding vertices of the pre-image and the image in the reflection.
5. The line segments connecting corresponding vertices are all congruent to each other.
- This statement is false. In reflections, the line segments connecting corresponding vertices can vary in length since they depend on the distance of each vertex from the line of reflection.
6. The line segments connecting corresponding vertices are all parallel to each other.
- This statement is false. In reflections, the line segments connecting corresponding vertices are not necessarily parallel to each other, as they converge towards the line of reflection.
Thus, the true statements about reflections are:
1. An image created by a reflection will always be congruent to its pre-image.
2. An image and its pre-image are always the same distance 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.
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
1. An image created by a reflection will always be congruent to its pre-image.
- This statement is true. In reflections, the shape and size of the image do not change, only its orientation does. Therefore, the image remains 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 true. By definition, a reflection in a line ensures that each 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.
- This statement is true. Any point that lies on the line of reflection does not move during the reflection. Hence, the point remains the same.
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- This statement is true. The line of reflection acts as a perpendicular bisector to the line segments that join corresponding vertices of the pre-image and the image in the reflection.
5. The line segments connecting corresponding vertices are all congruent to each other.
- This statement is false. In reflections, the line segments connecting corresponding vertices can vary in length since they depend on the distance of each vertex from the line of reflection.
6. The line segments connecting corresponding vertices are all parallel to each other.
- This statement is false. In reflections, the line segments connecting corresponding vertices are not necessarily parallel to each other, as they converge towards the line of reflection.
Thus, the true statements about reflections are:
1. An image created by a reflection will always be congruent to its pre-image.
2. An image and its pre-image are always the same distance 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.
4. The line of reflection is perpendicular to the line segments connecting corresponding vertices.
