IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.8 Congruence & Similarity

Syllabus Edition

First teaching 2021

Last exams 2024

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Congruence & Similarity (CIE IGCSE Maths: Extended)

Topic Questions

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1a
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cie-igcse-2020-may-jun-p4-tz2-q8a

Triangle ABC is mathematically similar to triangle PQR.
The area of triangle ABC is 16 cm2.

Calculate the area of triangle PQR.

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

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1b
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The triangles are the cross-sections of prisms which are also mathematically similar.
The volume of the smaller prism is 320 cm3.
 
Calculate the length of the larger prism.
 

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

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2
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Two cones are mathematically similar.
The total surface area of the smaller cone is 80 cm2.
The total surface area of the larger cone is 180 cm2.
The volume of the smaller cone is 168 cm3.

Calculate the volume of the larger cone.

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

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3
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cie-igcse-2019-oct-nov-p4-tz3-q6b

The diagram shows two mathematically similar solid metal prisms.
The volume of the smaller prism is 648 cm3 and the volume of the larger prism is 2187 cm3.
The area of the cross-section of the smaller prism is 36 cm2.

Calculate the area of the cross-section of the larger prism.
 

    
  

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

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4
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Two containers are mathematically similar.
The surface area of the larger container is 226 cm2 and the surface area of the smaller container is 94 cm2.
The volume of the larger container is 680 cm3.
 

Find the volume of the smaller container.
 

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

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5a
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cie-igcse-2020-oct-nov-p4-tz3-q5b

PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.

Explain why triangle PQR is similar to triangle PUT.
Give a reason for each statement you make.

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5b
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PT : TR = 4 : 3

i)
Find the ratio PU : PQ.
 
...................... : ...................... [1]
ii)
The area of triangle PUT is 20cm2.

Find the area of the quadrilateral QRTU.
  
.......................................... cm2 [3]

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1
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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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2
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Marianne sells two sizes of photo.
These photos are mathematically similar rectangles.
The smaller photo has length 15 cm and width 12 cm.
The larger photo has area 352.8 cm2.
 
Calculate the length of the larger photo.
 

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

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3
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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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4
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The diagram shows two cylinders, bold A and bold B

q6-paper2h-june2018-edexcel-igcse-maths

Cylinder bold A has height 1.6 m and radius 0.56 m.

Cylinder bold B is mathematically similar to cylinder bold A.
The height of cylinder bold B is 0.6 m.
Work out the radius of cylinder bold B.

....................................................... m

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5
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The diagram shows two water towers in Kuwait.

q7-paper1hr-jan2019-edexcel-igcse-maths

The real height of tower bold A is 187 straight m.
The real height of tower bold B is 147 straight m.

Ahmed makes a scale model of both towers.

The height of tower bold A on the scale model is 90 cm.

Work out the height of tower bold B on the scale model.
Give your answer correct to the nearest centimetre.

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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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cie-igcse-2020-may-jun-p4-tz3-q8c

A, B, C and D are points on the circle, centre O.
M is the midpoint of AB and N is the midpoint of CD.
OM = ON
 
Explain, giving reasons, why triangle OAB is congruent to triangle OCD.

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3
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Manjeet has two mathematically similar bottles in her bathroom.
The large bottle holds 1.35 litres and is 29.7 cm high.
The small bottle holds 0.4 litres.

Calculate the height of the small bottle.


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

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4
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cie-igcse-2019-may-jun-p4-tz2-q10c

The diagram shows two mathematically similar shapes with areas 295 space text cm end text squared and 159.5 space text cm end text squared.
The width of the larger shape is 17 space text cm end text.

Calculate the width of the smaller shape.
 

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

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5a
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cie-igcse-2019-march-p4-q6

The diagram shows a company logo made from a rectangle and a major sector of a circle.
The circle has centre O and radius OA.
OA = OD = 0.5 cm and AB = 1.5 cm.
E is a point on OC such that OE = 0.25 cm and angle OED = 90°.

Calculate the perimeter of the logo.
 

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

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5b
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Calculate the area of the logo.
 

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

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5c
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A mathematically similar logo is drawn.
The area of this logo is 77.44 cm2.

Calculate the radius of the major sector in this logo.
 

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

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6a
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cie-igcse-2018-oct-nov-p4-tz2-q10b

A solid metal cone has radius 10 cm and height 36 cm.

Calculate the volume of this cone.
[The volume, V, of a cone with radius r and height h is  V equals 1 third straight pi r squared h.]
 

 

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

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6b
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The cone is cut, parallel to its base, to give a smaller cone.

cie-igcse-2018-oct-nov-p4-tz2-q10bii

The volume of the smaller cone is half the volume of the original cone.

The smaller cone is melted down to make two different spheres.

The ratio of the radii of these two spheres is 1 : 2.


Calculate the radius of the smaller sphere.

[The volume, V, of a sphere with radius r is  V equals 4 over 3 straight pi r cubed.]

 

 

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

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