A real Pythagoras problem is a right triangle in disguise. The skill is undressing it: sketch the triangle, label the right angle, decide what you're hunting, then run the method you already know.
Story to Triangle
Take: “A telly is 14 cm across and 8 cm tall — how long is the diagonal?” Sketch a right triangle: the width and height are the two legs, the diagonal is the hypotenuse. You want the long slanted side, so add: d² = 14² + 8² = 196 + 64 = 260, then d = √260 ≈ 16.1 cm. The story never said “hypotenuse”, but the diagonal always is.
Working Backwards — the Reverse Case
This is the bit that proves you really get it. “A 5 m ladder leans against a wall, its foot 2 m out — how high does it reach?” Here the ladder is the hypotenuse (you already know it) and you want a shorter side, so you subtract: h² = 5² − 2² = 25 − 4 = 21, then h = √21 ≈ 4.6 m. Known hypotenuse plus one leg, working back to the other — that's the reverse of rung 1.
Always Sanity-check the Answer
Before you write it down, glance at it. A hypotenuse must be longer than either leg; a shorter side must be shorter than the hypotenuse. If a ladder “reaches” higher than its own length, you've added when you should have subtracted. That one check catches almost every mistake — and the toy works each problem through so the habit sticks.
Why This Is the Finish Line
Defining the theorem gave you the why; finding the hypotenuse and a shorter side gave you the how; spotting add-vs-subtract made it safe. Reading a real situation, drawing the triangle, choosing the right move and checking it — that's the whole loop, and it's exactly what Pythagoras is for. From here it carries into distances on a grid and, soon, trigonometry.