Use the distance formula to justify the congruence. The correct option is B.
.
<h3>Given, </h3>
the coordinates of
and
are ![A(0,0)\ B(4,0)\ C(1,3)\ D(5,2)\ E(8,5)\ F(8,1).](https://tex.z-dn.net/?f=A%280%2C0%29%5C%20B%284%2C0%29%5C%20C%281%2C3%29%5C%20D%285%2C2%29%5C%20E%288%2C5%29%5C%20F%288%2C1%29.)
The length of segment AC is
and the length of segment DF is also
.
and
.
We have to find the correct statement regarding the triangles to be congruent.
<h2>Distance formula</h2>
We know that, The distance formula to calculate the distance between two points
, and
is given as,
So, The distance between
and
Will be,
![FE=\sqrt{(8-8)^2+(5-1)^2} \\FE=\sqrt{4^2} \\FE=4\\](https://tex.z-dn.net/?f=FE%3D%5Csqrt%7B%288-8%29%5E2%2B%285-1%29%5E2%7D%20%5C%5CFE%3D%5Csqrt%7B4%5E2%7D%20%5C%5CFE%3D4%5C%5C)
Similarly, the distance between
and
will be,
![AB=\sqrt{(4-0)^2+(0-0)^2} \\AB=\sqrt{4^2} \\AB=4](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%284-0%29%5E2%2B%280-0%29%5E2%7D%20%5C%5CAB%3D%5Csqrt%7B4%5E2%7D%20%5C%5CAB%3D4)
So,
.......(1)
Now, in
and
,
( from equation 1 ).
( Given )
( Given )
So, By Side angle Side congruence rule,
.
Hence the correct option is B.
.
For more details on SAS congruence rule follow the link:
brainly.com/question/11804042