Which of the following reflective symmetries apply to the quadrilateral below

Symmetry
Applies to the figure?

Reflective symmetry over $\overline{B F}$
Yes/No

Reflective symmetry over $\overline{A D}$
Yes/No

Question

Which of the following reflective symmetries apply to the quadrilateral below

Symmetry
Applies to the figure?

Reflective symmetry over $\overline{B F}$
Yes/No

Reflective symmetry over $\overline{A D}$
Yes/No

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the line segments mentioned in the question: $\overline{BF}$ and $\overline{AD}$. ‖ ‖ step 2 ⋮ Determine if the quadrilateral has reflective symmetry over $\overline{BF}$. Reflective symmetry over $\overline{BF}$ means that the figure should be a mirror image on either side of $\overline{BF}$. ‖ ‖ step 3 ⋮ Check the given hash marks on the line segments. Since $\overline{AF}$, $\overline{AB}$, $\overline{BC}$, $\overline{DE}$, and $\overline{DC}$ all have two hash marks, it indicates that these segments are equal in length. ‖ ‖ step 4 ⋮ Analyze the symmetry over $\overline{BF}$. If $\overline{AF}$ and $\overline{AB}$ are equal, and $\overline{BC}$ and $\overline{DE}$ are equal, then the quadrilateral is symmetric over $\overline{BF}$. ‖ ‖ step 5 ⋮ Determine if the quadrilateral has reflective symmetry over $\overline{AD}$. Reflective symmetry over $\overline{AD}$ means that the figure should be a mirror image on either side of $\overline{AD}$. ‖ ‖ step 6 ⋮ Analyze the symmetry over $\overline{AD}$. Since $\overline{AF}$ and $\overline{AB}$ are equal, and $\overline{BC}$ and $\overline{DE}$ are equal, the quadrilateral is symmetric over $\overline{AD}$. ‖ ∻Answer∻ ***A*** ∻Key Concept∻ ⚹Reflective Symmetry⚹ ∻Explanation∻ ⚹Reflective symmetry means that one half of the figure is a mirror image of the other half. In this case, the quadrilateral has reflective symmetry over both $\overline{BF}$ and $\overline{AD}$ because the line segments on either side of these lines are equal in length.⚹◊What is the formula for reflective symmetry over a line $l$ in a 2D plane?⍭ Generate me a similar question◊

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