O LevelMathsCambridgeTopic QuestionsLengths, Areas & VolumesCongruence & Similarity

Congruence & Similarity (Cambridge O Level Maths)

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1
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q25-paper2-spec2025-cie-igcse-further-maths

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 spacecm.

Find the value of x.

x space equals space................

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2
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cie-igcse-2018-may-jun-2-p2-q11
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

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3
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Rectangle A B C D is mathematically similar to rectangle D A E F.

q4-hard-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

A B space equals space 10 space cm. space A D space equals space 4 space cm.

Work out the area of rectangle D A E F.

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1
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cie-igcse-2018-may-jun-3-p2-q25a

In the diagram, P Q is parallel to B C.
A P B and A Q C are straight lines.
P Q = 8 cm, B C = 10 cm and A B = 9cm.

Calculate P B.

P B = .......................................... cm

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2a
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screenshot-2023-05-26-at-4-26-02-pm

Quadrilaterals ABCD and LMNP are mathematically similar.

Angle A = angle L
Angle B = angle M
Angle C = angle N
Angle D = angle P

Work out the length of LP.

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2b
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Work out the length of BC.

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3
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q4-medium-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

A B C and A E D are straight lines.
B E and C D are parallel.
B E space equals space 1.5 space cm. space C D space equals space 6 space cm. space A D space equals space 5 space cm.

Calculate the length of E D.

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4
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cie-igcse-2018-oct-nov-p4-tz3-q8a

In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10 cm, CD = 5 cm, AX = 8 cm and BX = 6 cm.

Use similar triangles to calculate DX.

 

 

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

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5
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A solid cylinder with radius 1.6 cm is attached to the hemisphere to make a toy.

cie-igcse-2018-may-jun-1-6b

The total volume of the toy is 300 cm3.

A mathematically similar toy has volume 19 200 cm3.

Calculate the radius of the cylinder for this toy.


.......................................... cm

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6
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q10-specimen-paper1-2025-4024-01-cambridge-o-level-maths-d

The diagram shows a container in the shape of a prism with an open top.
The surface area of the inside of the container is 1340 cm2.

A mathematically similar container has a height of 16 cm.

Calculate the total surface area of the inside of the container with height 16 cm.

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

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1a
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cie-igcse-2020-oct-nov-p4-tz2-q8c

 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.

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1b
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AD  = 10 cm, BC  = 8 cm, BX  = 5 cm, CX  = 7 cm.  

Calculate DX.

 

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

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2
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The two triangles in the diagram are similar.

q4-veryhard-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

There are two possible values of x.

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

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3
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The diagram below shows two right-angled triangles.

q12-paper6-june2018-ocr-gcse-maths

Prove that triangles PQS and QRS are similar.

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