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

Soraya designs two mathematically similar flags.

Calculate the height, , of the larger flag.

= ............................................... m

The diagram shows two similar triangles, and  .

Calculate .

= ............................................. cm

Explain why triangle and triangle are similar.

Find .

= ............................. 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  and triangle  are similar.

Find .

= ............................... cm [2]

Are these two triangles definitely congruent?
Give a reason.

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

Circle the reason why these triangles are congruent.

The diagram shows two similar triangles and .

Calculate .

= ............................................ 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, , of the larger pot.

= ............................................ cm

Explain why triangle is similar to triangle .

Triangle is similar to triangle .

= ......................................... cm

Shape  is similar to shape .

Work out the value of .

................................

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 .

 is a quadrilateral.

. Angle
  = angle .

Prove that .