Congruence, Similarity & Geometrical Proof (Edexcel GCSE Maths: Foundation): Exam Questions

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.

[1]

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

[2]

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

Find $DE$.

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

Are these two triangles definitely congruent?
Give a reason.

..................... because ..............................................................................................................

Choose the reason why these triangles are congruent.

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 $a$.

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

ABC is an equilateral triangle.
D lies on BC.
AD is perpendicular to BC.

Prove that triangle ADC is congruent to triangle ADB.

Hence, prove that $BD=\frac{1}{2}AB$.

$ABCD$ is a quadrilateral.

$AB=CD$. Angle
$ABC$ = angle $BCD$.

Prove that $AC=BD$.