Similarity — Paper 1 · IGCSE Mathematics 0580

13 A B C 35o D NOT TO SCALE E In the diagram BC is parallel to DE. ABD and ACE are straight lines. (a) Choose one of the following words to complete the statement in the answer space. congruent equilateral isosceles similar Answer (a) Triangle ABC and triangle ADE are [1] (b) Angle BDE = 35°. Calculate the size of angle DBC. Answer (b) Angle DBC = [1]

2 marks

Mark scheme: 13 (a) similar 1 (b) 145 1

This question in 0580/11 May/June 2005

21 A cm 12 NOT TO SCALE B 68° D 8cm C 10 cm E In the diagram BC is parallel to DE. (a) Complete the following statement. Triangle ABC is to triangle ADE. [1] (b) AB = 12 cm, BC = 8 cm and DE = 10 cm. Calculate the length of AD. Answer(b) cm [2] (c) Angle ABC = 68°. Calculate the size of the reflex angle at D. Answer(c) [2]

5 marks

Mark scheme: 21 (a) Similar 1 (b) 15 2 M1 for 10 ÷ 8 × 12 or equivalent method (c) 292 2 M1 for 360 − 68

This question in 0580/11 Oct/Nov 2008

6 For F Examiner's Use NOT TO C SCALE 4 cm B 6 cm A E 15 cm D The triangles ABC and DEF are similar. AB = 6 cm, BC = 4 cm and DE = 15 cm. Calculate EF. Answer EF = cm [2]

2 marks

Mark scheme: 6 10 www 2 M1 for 15 ÷ 6 soi 6 15 or B1 for = oe or better 4 EF

This question in 0580/12 Oct/Nov 2010

22 46° NOT TO 9.65 cm SCALE 8.69 cm 9.65 cm x° 74° 60° y cm 46° 7.22 cm These two triangles are congruent. Write down the value of (a) x, Answer(a) x = … [1] (b) y. Answer(b) y = … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 22 (a) 74 1 (b) 8.69 1 IGCSE – May/June 2014 0580 13 5

This question in 0580/13 May/June 2014

22 B E NOT TO SCALE 8 cm 10 cm 6 cm x cm A y cm C D 9 cm F Triangle ABC is similar to triangle DEF. Calculate the value of (a) x, Answer(a) x = … [2] (b) y. Answer(b) y = … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 6 22 (a) 7.5 2 M1 for [10] × oe 8 8 10 (b) 12 cao 2 M1 for 9× oe or 9 × 6 their (a)

This question in 0580/11 May/June 2015

8 NOT TO SCALE 25 cm 15 cm 7.2 cm x cm The diagram shows two jugs that are mathematically similar. Find the value of x. Answer x = … [2]

2 marks

Mark scheme: 2.7 15 25 8 12 2 M1 for = oe or better eg 2.7 × x 25 15

This question in 0580/12 Oct/Nov 2015

21 A P NOT TO x cm 10 cm 7.5 cm SCALE 6.25 cm B 6 cm C Q y cm R The diagram shows two similar triangles ABC and PQR. Find the value of (a) x, Answer(a) x = … [2] (b) y. Answer(b) y = … [2] __________________________________________________________________________________________

4 marks

Mark scheme: x 10 21 (a) 12 nfww 2 M1 for = oe 5.7 .625 y .625 (b) 3.75 cao 2 M1 for = oe 6 10

This question in 0580/13 Oct/Nov 2015

13 Triangle ABC is similar to triangle PQR. Q B NOT TO SCALE 5.2 cm A C P R 12.4 cm 21.7 cm Find PQ. PQ = … cm [2]

2 marks

Mark scheme: 5.2 12.4 13 9.1 oe 2 M1 for = oe PQ 21.7  −1 

This question in 0580/12 Feb/March 2016

15 Triangle ABC and triangle DEF are similar. E NOT TO B SCALE 8.4 cm A 6 cm C D 15 cm F Calculate the length of EF. EF = … cm [2]

2 marks

Mark scheme: 15 21 2 M1 for 15 oe or 6 oe or 8.4 or 6 6 15 6 8.4 6 3 18 35 5

This question in 0580/11 May/June 2016

10 NOT TO x cm SCALE B 9 cm A 20 cm 12 cm Triangle A and triangle B are similar. Find the value of x. x = … [2]

2 marks

Mark scheme: 10 15 2 M1 for 20 ÷ 12 or 12 ÷ 9 or 9 ÷ 12 or 12 ÷ 20

This question in 0580/12 May/June 2016

17 (a) 80° 45° B A 35° C 55° D 55° 75° 80° NOT TO SCALE 55° Two of these triangles are similar. Write down the letters of these two triangles. … and … [1] (b) NOT TO h cm Q 4.2 cm P SCALE 9.6 cm 12.8 cm Rectangle P is similar to rectangle Q. Work out the value of h. h = … [2]

3 marks

Mark scheme: 17 (a) B and D 1 h 12.8 (b) 5.6 2 M1 for = oe or correct scale factor 4.2 9.6

This question in 0580/12 Oct/Nov 2016

11 Triangles ABC and DEF are similar. D A B E 16 cm x cm 12 cm 30 cm C NOT TO SCALE F Find the value of x. x = … [2]

2 marks

Mark scheme: x 30 x 16 11 40 2 M1 for = or = oe 16 12 30 12 16 or 2.5 or 0.4 or 1.33[3…] or 12

This question in 0580/13 Oct/Nov 2016

18 A NOT TO SCALE D 15 cm 5 cm B C E F 16.5 cm Triangles ABC and DEF are similar. Find the length of EF. EF = … cm [2]

2 marks

Mark scheme: 18 5.5 2 5 15 M1 for [× 16.5 ] or [16.5÷] or better 15 5

This question in 0580/12 May/June 2017

24 12 cm y cm NOT TO x cm 5 cm SCALE 15 cm 12.5 cm The two shapes are mathematically similar. Find the value of (a) x, x = … [2] (b) y. y = … [2]

4 marks

Mark scheme: 24(a) 6 2 15 12.5 12.5 5 M1 for or or or soi 12.5 15 5 12.5 24(b) 10 2 12.5 15 M1 for × 12 or 12 ÷ soi 15 12

This question in 0580/12 Oct/Nov 2017

12 P A 8 cm 14 cm NOT TO SCALE B Q 12 cm C x cm R Triangle ABC is similar to triangle PQR. Find the value of x. x = … [2]

2 marks

Mark scheme: 12 21 nfww 2 x 12 B1 for = oe, or better 14 8 4 or scale factor, i.e. 1.75 or oe seen 7

This question in 0580/11 Oct/Nov 2018

6 Triangle ABC and triangle DEF are similar. E NOT TO SCALE B 16 cm A C D F 18 cm 27 cm Find DE. DE = … cm [2]

2 marks

Mark scheme: 6 24 2 DE 16 M1 for = oe or scale factor, 1.5 27 18 2 or seen 3

This question in 0580/12 Oct/Nov 2018

18 The diagram shows a pentagon ABCDE. A E B D C (a) Using a straight edge and compasses only, construct the bisector of angle BCD. [2] (b) Draw the locus of the points inside the pentagon that are 3 cm from E. [1] (c) Shade the region inside the pentagon that is • less than 3 cm from E and • nearer to DC than to BC. [1]

4 marks

Mark scheme: 18(a) Correct ruled bisector with two pairs of 2 B1 for correct ruled bisector with arcs no/wrong arcs 18(b) Correct arc centre E radius 3 cm inside 1 pentagon 18(c) Correct region shaded 1 Dependent on at least B1 in part (a) and 1 mark in part (b) and a closed region

This question in 0580/12 Oct/Nov 2018

22 P A NOT TO 23 cm SCALE x cm B C Q R 8 cm 20 cm Triangle ABC is similar to triangle PQR. Find the value of x. x = … [2]

2 marks

Mark scheme: 22 9.2 2 x 23 M1 for = oe 8 20 2 or correct scale factor, 2.5 or seen 5

This question in 0580/13 Oct/Nov 2018

17 Q B 75° NOT TO 18 cm 75° SCALE 6 cm 65° 40° 65° 40° A C P R 27 cm (a) Explain why triangle ABC and triangle PQR are similar. … … [1] (b) Find AC. AC = … cm [2]

3 marks

Mark scheme: 17(a) angle A = angle P, 1 accept any two of these angle B = angle Q, or any other correct reason angle C = angle R 17(b) 9 2 M1 for 27 ÷ 3 18 6 18 27 or B1 for or or or 6 18 27 18 1 2 or for [sf=] 3 or or or 1.5 oe 3 3

This question in 0580/11 May/June 2019

18 Q 7.7 cm B C R NOT TO SCALE 5.5 cm P A a cm D 9.8 cm S Shape ABCD is similar to shape PQRS. Work out the value of a. a = … [2]

2 marks

Mark scheme: 18 7 2 5.5 7.7 9.8 7.7 M1 for or or or oe 7.7 5.5 7.7 9.8

This question in 0580/13 May/June 2019

21 A B C D E F G H The diagram shows some quadrilaterals. Complete the statements. (a) Quadrilateral … is a rhombus. [1] (b) Quadrilateral A is a … [1] (c) Quadrilaterals … and … are congruent. [1] (d) Quadrilaterals … and … are similar. [1]

4 marks

Mark scheme: 21(a) C 1 21(b) Trapezium 1 21(c) B and G 1 Both correct 21(d) D and F or B and G 1 Both correct

This question in 0580/12 Oct/Nov 2019

23 The scale drawing shows a triangle ABC. The scale is 1 centimetre represents 8 kilometres. B A C Scale : 1 cm to 8 km (a) Using a straight edge and compasses only, construct the bisector of angle BAC. Show all your construction arcs. [2] (b) Draw the locus of points inside triangle ABC that are 56 km from C. [2] (c) Shade the region inside triangle ABC that is • more than 56 km from C and • nearer to AC than to AB. [1]

5 marks

Mark scheme: 23(a) correct line with two correct pairs 2 B1 for correct line with no or incorrect arcs of correct arcs 23(b) arc centre C radius 7 cm and from 2 B1 for any arc centre C from AC to BC or arc AC to BC radius 7 cm from C not reaching AC and/or BC 23(c) correct region shaded 1 Dep on at least B1 B1

This question in 0580/13 Oct/Nov 2019

23 R 65° B NOT TO SCALE 78° Q 78° 37° A C P Explain why triangle ABC is similar to triangle PQR. … … [2] BLANK PAGE

2 marks

Mark scheme: 23 Angle ACB = 65˚ or M1 Angle RPQ = 37˚ 2 pairs of equal angles oe A1

This question in 0580/11 May/June 2020

23 U Y Z V 12 cm 63 cm NOT TO SCALE T 54 cm X The diagram shows two similar triangles TUV and XYZ. Calculate UT. UT = … cm [2]

2 marks

Mark scheme: 23 14 2 12 UT 54 63 M1 for = or = 54 63 12 UT 63 UT 54 12 or = or = or better 54 12 63 UT

This question in 0580/12 Oct/Nov 2020

17 P NOT TO A SCALE x cm 1.61 cm R 3.2 cm Q C 2.8 cm B Triangle ABC is mathematically similar to triangle PQR. Find the value of x. x = … [2]

2 marks

Mark scheme: 17 1.84 2 1.61 2.8 M1 for = oe x 3.2

This question in 0580/12 Feb/March 2021

20 NOT TO SCALE 12.5 cm 5 cm 32.5 cm 13 cm The diagram shows two cylinders. Show that the two cylinders are mathematically similar. [2]

2 marks

Mark scheme: 20 13 ÷ 5 = 2.6 2 M1 for 13 ÷ 5 = 2.6 or 32.5 ÷ 12.5 = 2.6 and 32.5 ÷ 12.5 = 2.6 or 32.5 ÷ 13 = 2.5 or 12.5 ÷ 5 = 2.5 or 32.5 ÷ 13 = 2.5 All are oe and 12.5 ÷ 5 = 2.5 or a correct pair of calculations without All are oe 2.6 or 2.5

This question in 0580/12 May/June 2021

22 E NOT TO B SCALE 85 cm 34 cm A C 28 cm D F Triangle ABC is similar to triangle DEF. Calculate DF. DF = … cm [2]

2 marks

Mark scheme: 22 70 2 DF 85 DF 28 M1 for = or = oe or better 28 34 85 34

This question in 0580/13 May/June 2021

4 A B C E D Write down the letter of the shape that is congruent to the shaded shape. … [1]

1 marks

Mark scheme: 4 E 1

This question in 0580/11 Oct/Nov 2021

24 C R NOT TO 6 cm SCALE A B P Q 8 cm 6 cm Triangle ABC is mathematically similar to triangle PQR. Calculate QR. QR = … cm [2]

2 marks

Mark scheme: 24 4.5 oe 2 8 6 M1 for oe or better 6 QR

This question in 0580/11 May/June 2022

3 On the grid, draw a triangle that is congruent to triangle A. A [1]

1 marks

Mark scheme: 3 A congruent triangle drawn 1

This question in 0580/12 May/June 2022

17 Q C NOT TO SCALE 9.2 cm 9.2 cm 7.3 cm A 7.3 cm B R P The diagram shows two right-angled triangles, ABC and PQR. (a) Complete this statement with a geometrical term. Triangle ABC is … to triangle PQR. [1] (b) Calculate angle ABC. Angle ABC = … [2]

3 marks

Mark scheme: 17(a) Congruent 1 17(b) 37.5 or 37.48 to 37.49 2 7.3 M1 for cos[ABC =] 9.2

This question in 0580/13 May/June 2022

21 A NOT TO D SCALE 51 cm 6 cm B C E F 4 cm Triangle ABC is mathematically similar to triangle DEF. Find BC. BC = … cm [2]

2 marks

Mark scheme: 21 34 2 BC 51 M1 for = oe or better 4 6

This question in 0580/11 Oct/Nov 2022

23 D A NOT TO h cm 5.6 cm SCALE B C E F 7.2 cm 8.1 cm Triangle ABC is similar to triangle DEF. Calculate the value of h. h = … [2]

2 marks

Mark scheme: 23 6.3 2 5.6 7.2 M1 for  oe or better h 8.1

This question in 0580/11 May/June 2023

21 NOT TO SCALE R C 9 cm A B P Q 15 cm 18 cm Triangle ABC is similar to triangle PQR. Calculate QR. QR = … cm [2]

2 marks

Mark scheme: 21 10.8 2 QR 18 M1 for  oe or better 9 15

This question in 0580/12 May/June 2023

24 B NOT TO E SCALE 7.3 cm x cm A 5.5 cm C D 4.4 cm F Triangle ABC is mathematically similar to triangle DEF. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 24 5.84 2 x 4.4 M1 for = oe or better 7.3 5.5

This question in 0580/12 Oct/Nov 2023

1 E B C A D Write down the letter of the shape that is congruent to the shaded shape. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 D 1

This question in 0580/13 Oct/Nov 2023

23 E B NOT TO SCALE h cm 97.5 cm A C 118.9 cm D 159.9 cm F Triangle ABC is mathematically similar to triangle DEF. Calculate the value of h. h = … [2]

2 marks

Mark scheme: 23 72.5 2 118.9 159.9 M1 for = oe or better h 97.5

This question in 0580/12 Feb/March 2024

24 A x cm NOT TO B SCALE 3.2 cm 6.75 cm 2.7 cm Shape A is mathematically similar to shape B. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 24 8 2 3.2 2.7 M1 for = oe or better x 6.75

This question in 0580/13 Oct/Nov 2024

25 Q B NOT TO 7 cm SCALE A 5 cm C P 10 cm R Triangle ABC is mathematically similar to triangle PQR. Show that QR = 14 cm. [1]

1 marks

Mark scheme: 25 10 1  7  = 14  oe 5

This question in 0580/12 Feb/March 2025

2 (a) Write down the mathematical name for an angle between 90° and 180°. … [1] (b) Write down the mathematical term that describes two polygons that are the same shape and size. … [1]

2 marks

Mark scheme: 2(a) Obtuse 1 2(b) Congruent 1

This question in 0580/13 May/June 2025

23 8 cm NOT TO SCALE 2 cm x cm 1.5 cm Rectangle A Rectangle B Rectangle A is mathematically similar to rectangle B. Work out the value of x. x = … [2]

2 marks

Mark scheme: 23 6 nfww 2 1.5 2 M1 for = oe or better x 8

This question in 0580/13 May/June 2025