Which theorem is repeatedly used in a square root spiral?

Correct answer: Pythagoras theorem

The direct answer is A: Pythagoras theorem. A square root spiral is made by constructing a sequence of right-angled triangles. In the first triangle, the two perpendicular sides can be taken as unit lengths, so the hypotenuse has length [?] No formula is needed to understand the idea: each new triangle uses the previous hypotenuse as one side and adds a new perpendicular side of one unit. The Pythagoras theorem connects the three sides of a right triangle through the relation \(c^2=a^2+b^2\), so it gives the next hypotenuse, such as \(\sqrt{2}\), \(\sqrt{3}\), and so on. Option A is correct because this repeated right-triangle calculation creates successive square-root lengths. Option B, the Remainder theorem, concerns the remainder obtained when a polynomial is divided by a linear expression; it is not the construction principle here. Option C, the Factor theorem, tests whether a value is a zero of a polynomial; it is unrelated to these triangles. Option D, the converse of Thales theorem, can help identify a right angle in some geometry situations, but it is not the theorem repeatedly used to calculate each new hypotenuse in the spiral. Exam cue: right triangle plus hypotenuse means think of Pythagoras.