Question

Math

Posted 4 months ago

```
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
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

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.

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