The image of trapezoid PQRS after a reflection across Line W Y is trapezoid P'Q'R'S'.

Question

2 trapezoids are shown. Line W Y is the line of reflection. Line segment R R prime has a midpoint at point Z. Line segment S S prime has a midpoint at point X.
What is the relationship between RR' and SS'?

RR' = 2SS'
RR' = 4SS'
RR' || SS'
RR' Perpendicular to SS'

Answer 1

In a reflection across a line, the segments connecting corresponding points (like \( RR' \) and \( SS' \)) will have certain relationships based on the properties of reflections.

1. Length Relationships: The length of the segments \( RR' \) and \( SS' \) will be equal because for any point and its reflection across a line, the distance from the point to the line is equal to the distance from the reflection point to the line. Therefore, \( RR' \) is equal to \( SS' \).

2. Parallelism: The segments \( RR' \) and \( SS' \) will be parallel to each other. This is due to the fact that all corresponding segments (perpendicular to the line of reflection) in symmetric figures remain parallel after reflection.

3. Perpendicularity: Since both segments are aligned with the same reflections, they are not perpendicular to each other unless specifically stated otherwise by the angles presented in the trapezoids, which isn’t given in your statement.

Given this, the most accurate answer among the choices provided is that \( RR' \) is parallel to \( SS' \), which can be expressed as:

RR' || SS'.