Answer and Explanation:
Given:
Part A: The equation for Triangle 2 is;
[tex]n^2=a^2+b^2[/tex]
Part B: Since;
[tex]\begin{gathered} a^2+b^2=c^2,\text{ and } \\ n^2=a^2+b^2 \\ Therefore, \\ c^2=n^2 \end{gathered}[/tex]
The resulting equation is c^2 = n^2
Part C: Let's take the square root of both sides from Part B;
[tex]\begin{gathered} \sqrt{c^2}=\sqrt{n^2} \\ c=n \end{gathered}[/tex]
The resulting equation is c = n
Part D:
By taking the square root in Part B we can see that side c and side n are equal in triangle 1 and triangle 2 respectively. So the equation is true.
Part E:
The relationship, c = n, shows that triangle 1 is also a right triangle because we have that side c is equal to the hypotenuse side n of the right triangle 2.