the graph shows triangles cde and vwx. is cde congruent to vwx? justify your answer. yes, because a rotation 180° around the origin maps cde onto vwx. yes, because a reflection across the y - axis maps cde onto vwx. no, because $ \overline { d e } $ and $ \overline { w x } $ do not have the same length. no, because $ \overline { c d } $ and $ \overline { v w } $ do not have the same length.

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Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{CD} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ C(8,2) $ and $ D(3,3) $, $ x_1 = 3,y_1 = 3,x_2 = 8,y_2 = 2 $.
$$
\begin{align*}
CD&=\sqrt{(8 - 3)^2+(2 - 3)^2}\
&=\sqrt{5^2+(-1)^2}\
&=\sqrt{25 + 1}\
&=\sqrt{26}
\end{align*}
$$
## Step2: Calculate the length of $ \overline{VW} $
For points $ V(-8,-2) $ and $ W(-4,-3) $, $ x_1=-8,y_1 = -2,x_2=-4,y_2=-3 $.
$$
\begin{align*}
VW&=\sqrt{(-4+8)^2+(-3 + 2)^2}\
&=\sqrt{4^2+(-1)^2}\
&=\sqrt{16+1}\
&=\sqrt{17}
\end{align*}
$$
Since $ CD=\sqrt{26}$ and $ VW=\sqrt{17}$, $ CD
eq VW $. Congruent triangles have all corresponding sides equal.

# Answer:
No, because $ \overline{CD} $ and $ \overline{VW} $ do not have the same length.

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Question

Explanation:

Step1: Calculate the length of \( \overline{CD} \)

Step2: Calculate the length of \( \overline{VW} \)

Answer: