Identify the hypotenuse
Locate the right angle and mark the side opposite it.
AQA 8300 · G20 · Right-triangle method
Pythagoras: choosing between adding and subtracting
The method-selection mark. Finding a shorter side needs a subtraction, and a solution that adds when it should subtract loses the method before the arithmetic starts.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Choose sum or difference
Add the squares for the hypotenuse; subtract for a shorter side.
Root and state units
Take the positive square root and give the length with its units.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Adding the two given squares regardless of which side is unknown — using a² + b² = c² when the missing length is a leg rather than the hypotenuse.
02
Why it survives revision
“Square, add, square root” is memorable, and it is right whenever the hypotenuse is the unknown, which is how the topic is introduced. The rule is never contradicted until the question changes which side is missing.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Find the right angle, mark the hypotenuse opposite it, then decide add or subtract. The decision comes before any squaring.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form puts the triangle inside a 3D solid or on a coordinate grid, where the right angle has to be located before the method can be chosen at all.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: G20 · Right-triangle method. Recognise Pythagoras from the diagram, then expose every square and root state. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
When do I subtract instead of add in Pythagoras?
Whenever the unknown side is a shorter side rather than the hypotenuse. Adding the two given squares is only correct when the hypotenuse is the one you are looking for.
How do I use Pythagoras in a 3D shape?
Find the right angle first — usually by identifying a right-angled triangle inside the solid — then apply the same method. Often it takes two applications, the first result feeding the second.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence