the graph shows quadrilaterals abcd and wxyz. is abcd congruent to wxyz? justify your answer. yes, because a reflection across the y - axis maps abcd onto wxyz. yes, because a translation right 10 units maps abcd onto wxyz. no, because $ \overline { bc } $ and $ \overline { xy } $ do not have the same length. no, because $ \angle a $ and $ \angle w $ do not have the same measure.

Question

Accepted Answer

# Explanation:
## Step1: Recall the definition of congruent figures
Congruent figures have all corresponding sides and angles equal.
## Step2: Check the length of $BC$ and $XY$
Using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for $B(-2,7)$, $C(-5,2)$
$$
\begin{align*}
BC&=\sqrt{(-2+5)^2+(7 - 2)^2}\
&=\sqrt{3^2+5^2}\
&=\sqrt{9 + 25}\
&=\sqrt{34}
\end{align*}
$$
For $X(1,7)$, $Y(5,2)$
$$
\begin{align*}
XY&=\sqrt{(1 - 5)^2+(7-2)^2}\
&=\sqrt{(-4)^2+5^2}\
&=\sqrt{16 + 25}\
&=\sqrt{41}
\end{align*}
$$
Since $BC
eq XY$, $ABCD$ is not congruent to $WXYZ$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the definition of congruent figures

Step2: Check the length of \(BC\) and \(XY\)

Answer: