the graph shows triangles lmn and uvw. is lmn congruent to uvw? justify your answer. yes, because a reflection across the y - axis maps lmn onto uvw. yes, because a translation right 11 units and up 2 units maps lmn onto uvw. no, because ∠l and ∠u do not have the same measure. no, because $ \overline{lm} $ and $ \overline{uv} $ do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{LM} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For $ L(-8,2) $ and $ M(-5,6) $, $ x_1=-8,y_1 = 2,x_2=-5,y_2 = 6 $.
$$
\begin{align*}
d_{LM}&=\sqrt{(-5+8)^2+(6 - 2)^2}\
&=\sqrt{3^2+4^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $ \overline{UV} $
For $ U(3,3) $ and $ V(5,7) $, $ x_1 = 3,y_1=3,x_2 = 5,y_2=7 $.
$$
\begin{align*}
d_{UV}&=\sqrt{(5 - 3)^2+(7 - 3)^2}\
&=\sqrt{2^2+4^2}\
&=\sqrt{4+16}\
&=\sqrt{20}\
&=2\sqrt{5}
\end{align*}
$$
Since $ 5
eq2\sqrt{5}$, $ \overline{LM}
eq\overline{UV} $. Congruent triangles have all corresponding sides equal.

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

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

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

Answer: