#### Answer

$(10, 13, 19)$ are not a Pythagorean Triple

#### Work Step by Step

The longest side is always the hypotenuse. $c=19$
Using the Pythagorean Theorem...
$a^{2}+b^{2}=c^{2}$
$10^{2}+13^{2}=19^{2}$
Simplify...
$100+169=361$
$269\ne361$
Since the equation is not true, the numbers $(10, 13, 19)$ are NOT a Pythagorean Triple.