CAIE IGCSE Mathematics Multi-Step Pythagoras Questions

Practise identifying right triangles inside larger diagrams and passing a Pythagoras result into the next geometric calculation.

Exam points

identify the right-angled subtriangle and calculate its missing side from squared lengths
use midpoint or preceding length information before carrying the result into a second step

[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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E6.1.1 Know and use Pythagoras’ theorem. question 1