Question

Find the lengths of the sides of the triangle to see if the two triangles are congruent.

Answer 1

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

`\begin{gathered} AB=√((3 - 0)^2 + (2 - 5)^2) \\ AB=√((3)^2 + (-3)^2) \\ AB=\sqrt{{9} + {9}} \\ AB=\sqrt[]{18} \\ \\ DE=√((4 - 1)^2 + (4 - 2)^2) \\ DE=√((3)^2 + (2)^2) \\ DE=\sqrt{{9} + {4}} \\ DE=\sqrt[]{13} \end{gathered}`

Side AC corresponds to side DF

`\begin{gathered} AC=√((1 - 0)^2 + (4 - 5)^2) \\ AC=√((1)^2 + (-1)^2) \\ AC=\sqrt{{1} + {1}} \\ AC=\sqrt[]{2} \\ \\ DF=√((7 - 1)^2 + (1 - 2)^2) \\ DF=√((6)^2 + (-1)^2) \\ DF=\sqrt{{36} + {1}} \\ DF=√(37) \end{gathered}`

Side BC corresponds to side EF

`\begin{gathered} BC=√((1 - 3)^2 + (4 - 2)^2) \\ BC=√((-2)^2 + (2)^2) \\ BC=\sqrt[]{4+4} \\ BC=\sqrt[]{8} \\ \\ EF=√((7 - 4)^2 + (1 - 4)^2) \\ EF=√((3)^2 + (-3)^2) \\ EF=\sqrt[]{9+9} \\ EF=\sqrt[]{18} \end{gathered}`

All the corresponding sides are not congruent, therefore the two triangles ΔABC, and ΔDEF are not congruent.