Syllabus Edition

First teaching 2021

Last exams 2024

|

Congruence & Similarity (CIE IGCSE Maths: Extended)

Exam Questions

2 hours34 questions
1
Sme Calculator
2 marks

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

cie-igcse-q12-similar-triangles

Find P Q.


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

Did this page help you?

2
Sme Calculator
1 mark

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

Did this page help you?

3
Sme Calculator
2 marks

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

Did this page help you?

4a
Sme Calculator
2 marks

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.

4b
Sme Calculator
2 marks

Work out the length of BC.

Did this page help you?

5
Sme Calculator
3 marks

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.

Did this page help you?

6
Sme Calculator
3 marks

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.

Did this page help you?

7a
Sme Calculator
2 marks

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.

7b
Sme Calculator
2 marks

AC = 6.15 cm.

Work out the length of AB.

Did this page help you?

1
Sme Calculator
3 marks

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 

Did this page help you?

2
Sme Calculator
3 marks

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

Did this page help you?

3
Sme Calculator
3 marks

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

Did this page help you?

4
Sme Calculator
2 marks

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

Did this page help you?

5
Sme Calculator
3 marks

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

Did this page help you?

6a
Sme Calculator
1 mark

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. 

6b
Sme Calculator
3 marks

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

Did this page help you?

1
Sme Calculator
3 marks

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

Did this page help you?

2
Sme Calculator
5 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

Did this page help you?

3
Sme Calculator
3 marks

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

Did this page help you?

4
Sme Calculator
2 marks

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.
 

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

Did this page help you?

5
Sme Calculator
5 marks

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.

Did this page help you?