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

Pick the word that describes two polygons that are the same shape and size.

On the grid, draw a shape that is congruent to shape $A$.

For the triangles shown on the grid, write down the letter of each triangle that is

i) congruent to triangle $X$,

ii) similar to triangle $X$.

The diagram shows four shapes $A,B,C$and $D$.

Which shapes, if any, are congruent to shape $D$?

Give a reason for your answer.

Quadrilaterals ................. and ................. are congruent.

Quadrilaterals ................. and ................. are similar.

Soraya designs two mathematically similar flags.

Calculate the height, $h$, of the larger flag.

$h$= ............................................... m

The diagram shows two similar triangles, $ABC$ and $DEF$.

Calculate $DF$.

$DF$ = ............................................. cm

Explain why triangle $ABC$ and triangle $PQR$ are similar.

Find $AC$.

$AC$ = ............................. cm

i) Explain why these rectangles are mathematically similar.

ii) How many times bigger is the area of the large rectangle than the area of the small rectangle?

Triangle $ABC$ and triangle $DEF$ are similar.

Find $DE$.

$DE$ = ............................... cm [2]

The diagram shows two similar triangles $TUV$ and $XYZ$.

Calculate $UT$.

$UT$ = ............................................ cm

The diagram shows two mathematically similar plant pots.

The smaller pot has height 21.6 cm and diameter 27 cm. The larger pot has diameter 33 cm.

Find the height, $h$, of the larger pot.

$h$ = ............................................ cm

Explain why triangle $ABC$ is similar to triangle $PQR$.

Triangle $ABC$ is similar to triangle $PQR$.

$PQ$ = ......................................... cm

Shape $ABCD$ is similar to shape $PQRS$.

Work out the value of $a$.

$a=$ ................................