We need to find whether the two given triangles are congruent.
The given triangles are congruent.
The distance between two points is given by
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A(2,-8) and B(-5,-2)
[tex]AB=\sqrt{(-5-2)^2+(-2-(-8))^2}\\\Rightarrow AB=\sqrt{49+36}\\\Rightarrow AB=\sqrt{85}[/tex]
D(-9,7) and E(-11,12)
[tex]DE=\sqrt{(-11-(-9))^2+(12-7)^2}\\\Rightarrow DE=\sqrt{29}[/tex]
B(-5,-2) and C(-7,3)
[tex]BC=\sqrt{(-7-(-5))^2+(3-(-2))^2}\\\Rightarrow BC=\sqrt{29}[/tex]
E(-11,12) and F(-2,1)
[tex]EF=\sqrt{(-2-(-11))^2+(1-12)^2}\\\Rightarrow EF=\sqrt{202}[/tex]
A(2,-8) and C(-7,3)
[tex]AC=\sqrt{(-7-2)^2+(3-(-8))^2}\\\Rightarrow AC=\sqrt{202}[/tex]
D(-9,7) and F(-2,1)
[tex]DF=\sqrt{(-2-(-9))^2+(1-7)^2}\\\Rightarrow DF=\sqrt{85}[/tex]
It can be seen that [tex]AB=DF=\sqrt{85}[/tex], [tex]BC=DE=\sqrt{29}[/tex] and [tex]AC=EF=\sqrt{202}[/tex].
Since, each side of triangle ABC is equal to one side of triangle DEF they are congruent to each other.
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