Congruence, Similarity & Geometrical Proof (Edexcel GCSE Maths: Foundation)

Exam Questions

43 mins21 questions
1
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1 mark

Pick the word that describes two polygons that are the same shape and size.

hexagon regular  perpendicular  congruent isosceles

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2
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1 mark

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On the grid, draw a shape that is congruent to shape A.

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3
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3 marks

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For the triangles shown on the grid, write down the letter of each triangle that is

i)
congruent to triangle X,
[1]
ii)
similar to triangle X.
[2]

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4
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1 mark

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The diagram shows four shapes space A comma space B comma space C spaceand D.

Which shapes, if any, are congruent to shape D?
Give a reason for your answer.

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5a
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1 mark

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Quadrilaterals ................. and ................. are congruent.

5b
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1 mark

Quadrilaterals ................. and ................. are similar.

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6
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1 mark

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Circle the reason why these triangles are congruent.

ASA          RHS   SAS    SSS

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7
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1 mark

Which of these is not used to prove that triangles are congruent?

Circle your answer.

SSS SAS AAA RHS

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1
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2 marks

Soraya designs two mathematically similar flags.

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Calculate the height, h, of the larger flag.

h space= ............................................... m

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2
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2 marks

The diagram shows two similar triangles, A B C and  D E F.

qp7d-0580-33-paper-3-oct-nov-2019-cie-igcse-maths

Calculate D F.

D F = ............................................. cm

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3a
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1 mark

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Explain why triangle A B C and triangle P Q R are similar.

3b
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2 marks

Find A C.

A C = ............................. cm

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4
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3 marks

q1a-058032-march2018-cie-igcse-maths-core

i)
Explain why these rectangles are mathematically similar.

[1]

ii)
How many times bigger is the area of the large rectangle than the area of the small rectangle?

[2]

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5
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2 marks

Triangle A B C and triangle D E F are similar.

q6-058012-octnov2018-cie-igcse-maths-core

Find D E.

D E = ............................... cm [2]

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6
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1 mark

Are these two triangles definitely congruent?
Give a reason.

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..................... because ..............................................................................................................

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7
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1 mark

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Circle the reason why these triangles are congruent.

SSS SAS ASA RHS

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1
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2 marks

qp23-0580-12-paper-1-nov-2020-cie-igcse-maths

The diagram shows two similar triangles T U V and X Y Z.

Calculate U T.

U T = ............................................ cm 

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2
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2 marks

The diagram shows two mathematically similar plant pots.

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The smaller pot has height 21.6 cm and diameter 27 cm.
The larger pot has diameter 33 cm.

Find the height, h, of the larger pot.

h = ............................................ cm

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3
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2 marks

qp23-0580-11-paper-1-may-2020-cie-igcse-maths

Explain why triangle A B C is similar to triangle P Q R.

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4
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2 marks

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

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P Q = ......................................... cm

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5
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2 marks

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Shape A B C D is similar to shape P Q R S.

Work out the value of a.

a space equals ................................

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6a
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3 marks

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ABC is an equilateral triangle.
D lies on BC.
AD is perpendicular to BC.

Prove that triangle ADC is congruent to triangle ADB.

6b
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2 marks

Hence, prove that B D equals 1 half A B.

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7
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4 marks

A B C D is a quadrilateral.

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A B space equals space C D.
Angle A B C = angle B C D.

Prove that A C equals space B D.

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