Given
ΔABC: A(0,5), B(3,2), C(1,4)
ΔDEF: D(1,2), E(4,4), F(7,1)
Solve for the corresponding sides and test if they are equal
Side AB corresponds to side DE
[tex]\begin{gathered} AB=\sqrt{(3 - 0)^2 + (2 - 5)^2} \\ AB=\sqrt{(3)^2 + (-3)^2} \\ AB=\sqrt{{9} + {9}} \\ AB=\sqrt[]{18} \\ \\ DE=\sqrt{(4 - 1)^2 + (4 - 2)^2} \\ DE=\sqrt{(3)^2 + (2)^2} \\ DE=\sqrt{{9} + {4}} \\ DE=\sqrt[]{13} \end{gathered}[/tex]
Side AC corresponds to side DF
[tex]\begin{gathered} AC=\sqrt{(1 - 0)^2 + (4 - 5)^2} \\ AC=\sqrt{(1)^2 + (-1)^2} \\ AC=\sqrt{{1} + {1}} \\ AC=\sqrt[]{2} \\ \\ DF=\sqrt{(7 - 1)^2 + (1 - 2)^2} \\ DF=\sqrt{(6)^2 + (-1)^2} \\ DF=\sqrt{{36} + {1}} \\ DF=\sqrt{37} \end{gathered}[/tex]
Side BC corresponds to side EF
[tex]\begin{gathered} BC=\sqrt{(1 - 3)^2 + (4 - 2)^2} \\ BC=\sqrt{(-2)^2 + (2)^2} \\ BC=\sqrt[]{4+4} \\ BC=\sqrt[]{8} \\ \\ EF=\sqrt{(7 - 4)^2 + (1 - 4)^2} \\ EF=\sqrt{(3)^2 + (-3)^2} \\ EF=\sqrt[]{9+9} \\ EF=\sqrt[]{18} \end{gathered}[/tex]
All the corresponding sides are not congruent, therefore the two triangles ΔABC, and ΔDEF are not congruent.
