Question

which of the following reflective symmetries apply to the parallelogram below? symmetry reflective symmetry over \\( \overline { c g } \\) reflective symmetry over \\( \overline { t h } \\) applies to the figure? yes/no yes/no

Explanation:

Step1: Recall the definition of reflective symmetry

Reflective symmetry means that when a figure is folded over a line (the line of symmetry), the two halves match exactly.

Step2: Analyze reflective symmetry over \( \overline{CG} \)

If we consider the line \( \overline{CG} \), the points on one side of \( \overline{CG} \) do not match the points on the other side of \( \overline{CG} \) in terms of distance from \( \overline{CG} \). For example, point \( A \) and its supposed mirror - image across \( \overline{CG} \) (if we assume reflective symmetry) do not coincide with the existing points of the parallelogram.

Step3: Analyze reflective symmetry over \( \overline{DH} \)

Similarly, for the line \( \overline{DH} \), the points on one side of \( \overline{DH} \) do not match the points on the other side of \( \overline{DH} \) in terms of distance from \( \overline{DH} \). A parallelogram (that is not a rhombus, rectangle or square) has no lines of reflective symmetry.

Answer:

Reflective symmetry over \( \overline{CG} \): No
Reflective symmetry over \( \overline{DH} \): No