4. Which two sides of the triangle ABC are congruent?"6B(5.5)C-1,3)22 3 4 5 6 7 8-2A(4.-2)68

Triangle ABC
A(4,-2)
B(5,5)
C(-1,3)
To calculate each side length you have to apply the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]Considering each side of the triangle as the hypothenuse of a rigth triangle you can say that their base and heigth will be determined by their coordinates over the x and y axis so that:
[tex]\begin{gathered} a=(x_2-x_1) \\ b=(y_2-y_1) \end{gathered}[/tex]Then:
[tex]c^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]Finally:
[tex]c=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Side AB
c=AB
A(4,-2) B(5,5)
[tex]\begin{gathered} AB^{}=\sqrt[]{(5-4)^2+(5-(-2))^2} \\ AB=5\sqrt[]{2} \end{gathered}[/tex]Side BC
c=BC
B(5,5) C(-1,3)
[tex]\begin{gathered} BC=\sqrt[]{(5-(-1))^2+(5-3)^2} \\ BC=2\sqrt[]{10} \end{gathered}[/tex]Side AC
c= AC
A(4,-2) C(-1,3)
[tex]\begin{gathered} AC=\sqrt[]{(4-(-1))^2+(-2-3)^2} \\ AC=5\sqrt[]{2} \end{gathered}[/tex]Acording to the calculated lengths AB≅AC
The correct option is a)