1. The problem asks: In which triangle(s) can you apply Pythagoras' Theorem? 2. Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse ($c$) equals the sum of the squares of the other two sides ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. Important rule: Pythagoras' Theorem only applies to right-angled triangles. 4. Diagram A shows a right-angled triangle with a right-angle marker. 5. Diagram B shows a triangle without a right-angle marker, so we cannot confirm it is right-angled. 6. Diagram C shows a right-angled triangle with equal side tick marks on the legs and a right angle indicated. 7. Diagram D shows a right-angled triangle with equal side tick marks on the two shorter sides and a right angle indicated. 8. Therefore, Pythagoras' Theorem can be applied to Diagrams A, C, and D because they have right angles. Final answer: Diagrams A, C, and D are right-angled triangles where Pythagoras' Theorem applies.