Question

Independent work Verifying right trianglesVerifying a Right Triangle.Show that the points (1, 0), (13,5), and (13, 0) are vertices of a right triangle.(a) Find the length of each side of the right triangle,and (b) show that these lengths satisfy the Pythagorean Theorem.

Answer 1

1) Since the points are: A(1, 0), B(13,5), and C(13, 0)

a) To find the length of each leg

$\begin{gathered} d_{AB}\text{ =}\sqrt{(13-1)^2+(5-0)^2}\text{ = }13 \\ d_{BC}=\sqrt{(13-13)^2+(0-5)^2}\text{ =}\sqrt{0\text{ +25}}\text{ = 5} \\ d_{CA\text{ =}}\sqrt{(13-1)^2+(0-0)^2}\text{ =}\sqrt{144}\text{ = 12} \end{gathered}$

b) Show that these satisfy to the Pythagorean Theorem

Note, a triangle 5,12,13 is a classic Pythagorean triangle, but let's prove it.

This identity must be true on both sides, to prove it. Let's pick the greater side, the hypotenuse = 13 plug it and the other legs as well:

a² =b²+c²

13² = 5²+12²

169 = 25 +144

169 = 169 True