Question

Math

Posted 3 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 3 months ago

Solution by Steps

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 $\overline{AD}$.

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