Answer:
CD ≠ EF
Step-by-step explanation:
Using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = C(- 2, 5) and (x₂, y₂ ) = D(- 1, 1)
CD = [tex]\sqrt{(-1+2)^2+(1-5)^2}[/tex]
= [tex]\sqrt{1^2+(-4)^2}[/tex]
= [tex]\sqrt{1+16}[/tex] = [tex]\sqrt{17}[/tex]
Repeat using (x₁, y₁ ) = E(- 4, - 3) and (x₂, y₂ ) = F(- 1, - 1)
EF = [tex]\sqrt{(- 1+4)^2+(-1+3)^2}[/tex]
= [tex]\sqrt{3^2+2^2}[/tex]
= [tex]\sqrt{9+4}[/tex] = [tex]\sqrt{13}[/tex]
Since [tex]\sqrt{17}[/tex] ≈ [tex]\sqrt{13}[/tex] , then CD and EF are not congruent
