CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.8 Congruence & Similarity

Syllabus Edition

First teaching 2021

Last exams 2024

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3.8 Congruence & Similarity

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1
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A paperweight has height 4 cm and volume 38.4 cm3.
A mathematically similar paperweight has height 7 cm.
 
Calculate the volume of this paperweight.
 

 .......................................... cm3 

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2
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Two mathematically similar containers have heights of 30 cm and 75 cm.
The larger container has a capacity of 5.5 litres.

Calculate the capacity of the smaller container.
Give your answer in millilitres.

............................................... ml

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3
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A model of a car has a scale 1:20.
The volume of the actual car is 12 m3.

Find the volume of the model.
Give your answer in cubic centimetres.
 

......................................cm3

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4
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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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5
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cie-igcse-2018-may-jun-3-p2-q25b

The diagram shows two glasses which are mathematically similar.
The larger glass has a capacity of 0.5 litres and the smaller glass has a capacity of 0.25 litres.
The height of the larger glass is 13 cm.

Calculate the height of the smaller glass.

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

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6a
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cie-igcse-2018-march-p2-14

A, B, C and D are points on the circumference of the circle.
AC and BD intersect at X.

Complete the statement.


Triangle ADX is ..................................................... to triangle BCX. 

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6b
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The area of triangle ADX is 36 cm2 and the area of triangle BCX is 65.61 cm2.
AX = 8.6 cm and DX = 7.2 cm.

Find BX.


BX = .................................. cm

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1
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Triangle A B C is similar to triangle P Q R.

cie-igcse-q12-similar-triangles

Find P Q.


P Q space equals ......................................... cm

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2
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LQsU3UnO_cie-igcse-2018-oct-nov-p2-tz1-q2

In the diagram, AB = AC and BN = NC.

Complete the statement using a mathematical term.
 

Triangle ABN is ...................................... to triangle ACN

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3
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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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4a
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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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4b
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Work out the length of BC.

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5
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A B C and A B D are two right-angled triangles.

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

Angle space B A C space equals space angle space A D B space equals space 90 degree A B space equals space 13 space cm space D B space equals space 5 space cm

Work out the length of C B.

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6
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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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7a
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screenshot-2023-05-26-at-4-54-15-pm

ABC and EDC are straight lines.
EA is parallel to DB.

EC = 8.1 cm.
DC = 5.4 cm.
DB = 2.6 cm,

Work out the length of AE.

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7b
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AC = 6.15 cm.

Work out the length of AB.

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1
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A model of a statue has a height of 4cm.
The volume of the model is 12 cm3.
The volume of the statue is 40 500 cm3.

Calculate the height of the statue.


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

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2
Sme Calculator5 marks

cie-igcse-2020-may-june-p2-tz1-q13

C lies on a circle with diameter A D.
B lies on A C and E lies on A D such that B E is parallel to C D.
A B = 21 cm, C D = 18 cm and B E = 13.5 cm.

Work out the radius of the circle.


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

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3
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cie-igcse-2020-mary-jun-p2-tz3-q17

The diagram shows two shapes that are mathematically similar.
The smaller shape has area 52.5 cm2 and the larger shape has area 134.4 cm2.
 
Calculate the value of m.
 

m equals................................................

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4
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The area of pentagon A is 73.5 space text cm end text squared.
The area of pentagon B is 6 space text cm end text squared.

Find the ratio    perimeter of pentagon A : perimeter of pentagon B   in its simplest form.
 

......................... : .........................

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5
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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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