Question

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

Answer 1

Triangle ABC

A(4,-2)

B(5,5)

C(-1,3)

To calculate each side length you have to apply the Pythagoras theorem:

$a^2+b^2=c^2$

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:

$\begin{gathered} a=(x_2-x_1) \\ b=(y_2-y_1) \end{gathered}$

Then:

$c^2=(x_2-x_1)^2+(y_2-y_1)^2$

Finally:

$c=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

Side AB

c=AB

A(4,-2) B(5,5)

$\begin{gathered} AB^{}=\sqrt[]{(5-4)^2+(5-(-2))^2} \\ AB=5\sqrt[]{2} \end{gathered}$

Side BC

c=BC

B(5,5) C(-1,3)

$\begin{gathered} BC=\sqrt[]{(5-(-1))^2+(5-3)^2} \\ BC=2\sqrt[]{10} \end{gathered}$

Side AC

c= AC

A(4,-2) C(-1,3)

$\begin{gathered} AC=\sqrt[]{(4-(-1))^2+(-2-3)^2} \\ AC=5\sqrt[]{2} \end{gathered}$

Acording to the calculated lengths AB≅AC

The correct option is a)