here are the endpoints of the segments $ \overline { a b } $, $ \overline { c d } $, and $ \overline { e f } $.
$ a ( - 8,1 ) , b ( - 5,6 ) $
$ c ( - 3,0 ) , d ( - 7 , - 5 ) $
$ e ( 5,3 ) , f ( 7 , - 4 ) $
follow the directions below.
(a) find the length of each segment.
give an exact answer (not a decimal approximation).
$ a b = $
$ c d = $
$ e f = $
(b) check all statements that are true below.
$ \square \overline { a b } \cong \overline { c d } $
$ \square \overline { a b } \cong \overline { e f } $
$ \square \overline { c d } \cong \overline { e f } $
$ \square $ none of these are true

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of segment $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $A(-8,1)$ and $B(-5,6)$, $x_1=-8,y_1 = 1,x_2=-5,y_2 = 6$.
$$
\begin{align*}
AB&=\sqrt{(-5-(-8))^2+(6 - 1)^2}\
&=\sqrt{(3)^2+(5)^2}\
&=\sqrt{9 + 25}\
&=\sqrt{34}
\end{align*}
$$
## Step2: Calculate the length of segment $CD$
For $C(-3,0)$ and $D(-7,-5)$, $x_1=-3,y_1 = 0,x_2=-7,y_2=-5$.
$$
\begin{align*}
CD&=\sqrt{(-7-(-3))^2+(-5 - 0)^2}\
&=\sqrt{(-4)^2+(-5)^2}\
&=\sqrt{16+25}\
&=\sqrt{41}
\end{align*}
$$
## Step3: Calculate the length of segment $EF$
For $E(5,3)$ and $F(7,-4)$, $x_1=5,y_1 = 3,x_2=7,y_2=-4$.
$$
\begin{align*}
EF&=\sqrt{(7 - 5)^2+(-4 - 3)^2}\
&=\sqrt{(2)^2+(-7)^2}\
&=\sqrt{4 + 49}\
&=\sqrt{53}
\end{align*}
$$
## Step4: Check the congruence of segments
Since $AB=\sqrt{34}$, $CD=\sqrt{41}$, $EF=\sqrt{53}$, and $\sqrt{34}
eq\sqrt{41}
eq\sqrt{53}$

# Answer:
(a) $AB=\sqrt{34}$, $CD=\sqrt{41}$, $EF=\sqrt{53}$

(b) None of these are true

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of segment \(AB\)

Step2: Calculate the length of segment \(CD\)

Step3: Calculate the length of segment \(EF\)

Step4: Check the congruence of segments

Answer: