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 ⋮ To determine reflective symmetry over $\overline{BF}$, we need to check if the quadrilateral is mirrored across line $\overline{BF}$. ‖ ‖ step 2 ⋮ Since $\overline{AF}$ is equal to $\overline{AB}$ and $\overline{ED}$ is equal to $\overline{DC}$, if $\overline{BF}$ is a line of symmetry, then $\overline{AD}$ should be equal to $\overline{BC}$ and $\overline{AE}$ should be equal to $\overline{EC}$. ‖ ‖ step 3 ⋮ However, there is no information given that suggests $\overline{AD}$ is equal to $\overline{BC}$ or $\overline{AE}$ is equal to $\overline{EC}$. Therefore, reflective symmetry over $\overline{BF}$ does not apply to the figure. ‖ ‖ step 4 ⋮ To determine reflective symmetry over $\overline{AD}$, we need to check if the quadrilateral is mirrored across line $\overline{AD}$. ‖ ‖ step 5 ⋮ Given that $\overline{AF}$ is equal to $\overline{AB}$ and point D is the midpoint of $\overline{AC}$ (since it connects to all other vertices), it suggests that $\overline{AD}$ could be a line of symmetry. ‖ ‖ step 6 ⋮ However, since $\overline{ED}$ is equal to $\overline{DC}$ and there is no information suggesting that $\overline{AE}$ is equal to $\overline{EC}$, reflective symmetry over $\overline{AD}$ does not apply to the figure. ‖ ∻1 Answer∻ ***No, No*** ∻Key Concept∻ ⚹Reflective Symmetry⚹ ∻Explanation∻ ⚹Reflective symmetry in a figure means that one half of the figure is a mirror image of the other half across a line of symmetry. The given information does not support the existence of reflective symmetry over either $\overline{BF}$ or $\overline{AD}$.◊What is the formula to calculate the distance between two points in a coordinate⍭ Generate me a similar question◊⚹

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