CAIE IGCSE Mathematics Extended Pythagoras Problems

Practise applying Pythagoras' theorem after deriving intermediate lengths from midpoint, similarity or other geometric information.

Exam points

derive the required right-triangle sides from midpoint, ratio or diagram information first
apply Pythagoras in one or more linked right triangles and preserve intermediate accuracy

Covered syllabus points

E6.1.1 Know and use Pythagoras’ theorem.

[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 $AB=18\cos60^\circ$
M1
$\cos60^\circ=\frac{1}{2}$ and AB=9
A1
Correct use of Pythagoras' theorem, i.e. $CD^2=6^2+(17-\text{their }AB)^2$ oe
M1
Correct evaluation for their AB: $CD^2=36+64$ or $CD=\sqrt{36+64}$
M1
100=10
A1

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Covered syllabus points

E6.1 Pythagoras’ theorem question 1