CAIE IGCSE Mathematics Extended E6.1.1 Know and Use Pythagoras Theorem Questions

Practise Extended CAIE IGCSE Mathematics by identifying right-angled triangles and calculating missing sides with a² + b² = c².

Exam points

Use Pythagoras’ theorem to calculate a missing side in a right-angled triangle.
Identify the hypotenuse and apply a² + b² = c² correctly.
Rearrange and interpret Pythagorean calculations in geometric problems.

[Maximum number: 5]

The quadrilateral ACDE is formed by two right-angled triangles ABE and BCD. $A C=17 \mathrm{~cm}, A E=18 \mathrm{~cm}$ and $B D=6 \mathrm{~cm}$ .

Show that $C D=10 \mathrm{~cm}$ .

$\frac{AB}{18}=\cos60^\circ$ or $AB=18\cos60^\circ$ $\cos60^\circ=\frac{1}{2}$ and AB=9
Correct use of Pythagoras' theorem, i.e. $CD^2=6^2+(17-\text{their }AB)^2$ oe
Correct evaluation for their AB: $CD^2=36+64$ or $CD=\sqrt{36+64}$ 100=10

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CAIE IGCSE Mathematics Extended E6.1.1 Know and Use Pythagoras Theorem Questions question 1