Shape and Space 3
4 marks · HardExplain, using step-by-step reasoning and a diagram, how you would use Pythagoras’ Theorem to check whether a triangle with sides 10 cm, 16 cm, and 18 cm is a right-angled triangle.
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Draw a triangle with sides 10 cm, 16 cm, 18 cm, identify the largest side (18 cm) as the possible hypotenuse. Use Pythagoras' Theorem to check if 10² + 16² = 18². If so, it is right-angled at the vertex opposite the 18 cm side.
Must show: Identification of the hypotenuse, Setting up of squares of all sides, Comparison of the sum of squares, Conclusion, A labelled triangle diagram
Common mistakes: Not identifying the hypotenuse; Comparing the wrong pairs of sides; Arithmetic mistakes in squaring
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Marking points
B1 · 1 mark · Draws and labels a triangle with sides 10 cm, 16 cm, 18 cm.
M1 · 1 mark · Identifies the largest side (18 cm) as potential hypotenuse.
M2 · 1 mark · Correctly calculates: 10² + 16² = 100 + 256 = 356; 18² = 324.
A1 · 1 mark · Compares and clearly concludes triangle is not right-angled, since 356 ≠ 324. (follow-through)
Worked solution
Step 1: Draw the triangle and label the sides 10 cm, 16 cm, 18 cm. The longest side (18 cm) is the possible hypotenuse.
Step 2: Use Pythagoras' Theorem: for a right-angled triangle, (hypotenuse)² = (side 1)² + (side 2)².
Since 356 ≠ 324, the triangle is not right-angled.