1. **State the problem:** We need to determine if the triangles EFG and TUV are right-angled using Pythagoras' theorem. 2. **Recall Pythagoras' theorem:** For a triangle with sides $a$, $b$, and hypotenuse $c$, the triangle is right-angled if and only if $$a^2 + b^2 = c^2$$ where $c$ is the longest side. 3. **Triangle EFG:** The sides are 18 cm, 24 cm, and 30 cm. The longest side is 30 cm. Calculate $$18^2 + 24^2 = 324 + 576 = 900$$ Calculate $$30^2 = 900$$ Since $$18^2 + 24^2 = 30^2$$, triangle EFG is right-angled. 4. **Triangle TUV:** The sides are 14 cm, 20 cm, and 24 cm. The longest side is 24 cm. Calculate $$14^2 + 20^2 = 196 + 400 = 596$$ Calculate $$24^2 = 576$$ Since $$14^2 + 20^2 \neq 24^2$$, triangle TUV is not right-angled. **Final answer:** Triangle EFG is right-angled, and triangle TUV is not right-angled.