Read it again any time, including while you work through the exercises.
You already know the Pythagorean theorem: in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It lets you compute a length when you know the right angle is there. But flip the question: what if you only know the three lengths? Can you prove the triangle is right-angled, without a set square, without measuring any angle? Yes, thanks to the converse.
The converse of the Pythagorean theorem says this: if, in a triangle, the square of the longest side equals the sum of the squares of the other two, then the triangle is right-angled. And the right angle sits opposite the longest side. It is a proof tool: numbers alone are enough to guarantee the right angle, no visual check needed.
This idea is very old and very concrete: Egyptian builders used a rope with 13 knots forming 12 equal intervals. Stretching it into a triangle with sides 3, 4 and 5, they obtained a perfectly right angle for their foundations. Why? Because 3² + 4² = 9 + 16 = 25 = 5². The rope proved the right angle, exactly like the converse.
The method takes three moves: spot the longest side, compute separately its square then the sum of the squares of the other two, and compare. Equal? Right triangle. Not equal? Not right-angled, and the theorem proves that too. Be careful never to mix up the direct statement (I know it is right-angled, I compute) and the converse (I compute to prove it is right-angled). That is exactly what we are going to practice.