Answer
a) 12; 5; 13;
b) The three sides verify the Pythagorean Theorem.
Work Step by Step
a) Find the length of each side of the right triangle:
$\sqrt{(13-1)^2+(0-0)^2}=\sqrt{144}=12$
$\sqrt{(13-13)^2+(5-0)^2}=\sqrt{25}=5$
$\sqrt{(13-1)^2+(5-0)^2}=\sqrt{169}=13$
b) Check that the sides verify the Pythagorean Theorem:
$12^2+5^2\stackrel{?}{=}13^2$
$144+25\stackrel{?}{=}169$
$169=169\checkmark$
