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Congruence & Similarity (Cambridge O Level Maths)

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Congruence & Similarity

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Congruence & Similarity

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1
Sme Calculator2 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

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2a
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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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2b
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AC = 6.15 cm.

Work out the length of AB.

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3
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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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4
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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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5
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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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6
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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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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-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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5a
Sme Calculator1 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. 

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5b
Sme Calculator3 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

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6a
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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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6b
Sme Calculator4 marks

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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7a
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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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7b
Sme Calculator2 marks

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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8
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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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9
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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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10
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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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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
Sme Calculator2 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.
 

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

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5
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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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6
Sme Calculator3 marks

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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7a
Sme Calculator5 marks

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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7b
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Calculate the area of the logo.
 

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

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7c
Sme Calculator3 marks

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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8a
Sme Calculator2 marks

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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8b
Sme Calculator4 marks

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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9
Sme Calculator5 marks

q8b-june-2021-4024-21-cambridge-o-level-maths-d

Triangle space K L M spaceis similar to triangle K N J.
 J K M and space N K L spaceare straight lines.

space K L with hat on top M space equals space K N with hat on top J andspace L K with hat on top M space equals space y degree.

 K L space equals space 6 space cm, K M space equals space 10.5 cm and K N space equals space 10 space cm.
The area of triangle J K N is 75 cm2.
Calculate y.

y= ................................

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