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Using Pythagoras' theorem in 2D

Geometry · Grade 4–6

Strand: Geometry Substrand: Pythagoras' theorem Sparx code: U385 Sparx levels: 1, 2, 3, 4, 5

Key steps (method)

  • Write down a² + b² = c² (c is the hypotenuse).
  • Identify the hypotenuse correctly (the side opposite the right angle).
  • Substitute the known lengths and solve for the unknown.
  • If you’re finding a shorter side, rearrange: a² = c² − b².
  • Check the result is sensible (hypotenuse should be the longest).

Common mistakes

  • Using the wrong side as the hypotenuse.
  • Adding instead of subtracting when finding a shorter side.
  • Forgetting to square-root at the end.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Using Pythagoras' theorem in 2D (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes