Congruence & Similarity (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

The two shapes are mathematically similar.
The area of the larger shape is 36 cm² and the area of the smaller shape is 25 cm².
The height of the larger shape is 9 cm and the height of the smaller shape is $x$cm.

Find the value of $x$.

$x=................$

The diagram shows two mathematically similar triangles, T and U.
Two corresponding side lengths are 3 cm and 12 cm. The area of triangle T is 5 cm².

Find the area of triangle U.

......................................... cm²

Rectangle $ABCD$ is mathematically similar to rectangle $DAEF$.

$\begin{array}{l}AB=10\mathrm{cm}.\\ AD=4\mathrm{cm}.\end{array}$

Work out the area of rectangle $DAEF$.

The two shapes are mathematically similar.
The area of the larger shape is 36 cm² and the area of the smaller shape is 25 cm².
The height of the larger shape is 9 cm and the height of the smaller shape is $x$cm.

Find the value of $x$.

$x=................$

The diagram shows two mathematically similar triangles, T and U.
Two corresponding side lengths are 3 cm and 12 cm. The area of triangle T is 5 cm².

Find the area of triangle U.

......................................... cm²

Rectangle $ABCD$ is mathematically similar to rectangle $DAEF$.

$\begin{array}{l}AB=10\mathrm{cm}.\\ AD=4\mathrm{cm}.\end{array}$

Work out the area of rectangle $DAEF$.

 The diagonals of the cyclic quadrilateral ABCD intersect at X.  

Explain why triangle ADX is similar to triangle BCX. Give a reason for each statement you make.

AD  = 10 cm, BC  = 8 cm, BX  = 5 cm, CX  = 7 cm.  

Calculate DX.

DX = ........................................... cm

The two triangles in the diagram are similar.

There are two possible values of $x$.

Work out each of these values.
State any assumptions you make in your working.

The diagram below shows two right-angled triangles.

Prove that triangles PQS and QRS are similar.

The two triangles in the diagram are similar.

There are two possible values of $x$.

Work out each of these values.
State any assumptions you make in your working.

The diagram below shows two right-angled triangles.

Prove that triangles PQS and QRS are similar.