GeometryGeometrical terms
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2 NOT TO SCALE A B C N In the diagram, AB = AC and BN = NC. Complete the statement using a mathematical term. Triangle ABN is ...................................... to triangle ACN. [1]
IGCSE Mathematics 0580 · Topic practice
Work through angle properties, polygons, circle theorems, similarity and constructions. Name the property you used for each angle, because the reason is often worth a mark of its own.
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You’re practising 2016–2018 papers. The 2019–2026 papers, including 2026, need a plan.
Unlock from $6/mo2 NOT TO SCALE A B C N In the diagram, AB = AC and BN = NC. Complete the statement using a mathematical term. Triangle ABN is ...................................... to triangle ACN. [1]
2 A D O M NOT TO SCALE N E B The diagram shows a circle, centre O. AB and DE are chords of the circle. M is the mid-point of AB and N is the mid-point of DE. AB = DE = 9 cm and OM = 5 cm. Find ON. ON = ......................................... cm [1]
5 x° 43° Q T C B S P A NOT TO SCALE The diagram shows two parallel lines PAQ and SBCT. AB = AC and angle QAC = 43°. Find the value of x. x = ....................................... [2]
5 The diagram shows a regular pentagon and a kite. Complete the following statements. (a) The regular pentagon has ................................... lines of symmetry. [1] (b) The kite has rotational symmetry of order ................................... . [1]
6 NOT TO SCALE B A North The bearing of A from B is 227°. Find the bearing of B from A. ................................................. [2]
7 A and B are two towns on a map. The bearing of A from B is 140°. Work out the bearing of B from A. ................................................. [2]
9 Using a straight edge and compasses only, construct the locus of points that are equidistant from A and B. A B [2]
11 3 cm 12 cm U T NOT TO SCALE 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 [2]
13 A C B The diagram shows a triangle ABC and an arc with centre C and radius 6.5 cm. (a) Using a straight edge and compasses only, construct the locus of points inside the triangle that are equidistant from BA and BC. [2] (b) Shade the region inside the triangle that is • more than 6.5 cm from C and • nearer to BA than to BC. [1]
14 D B X A C NOT TO SCALE A, B, C and D are points on the circumference of the circle. AC and BD intersect at X. (a) Complete the statement. Triangle ADX is ..................................................... to triangle BCX. [1] (b) 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 [3]
15 58° 63° b° a° NOT TO SCALE Complete the statements. a = ............................................... because .................................................................................................. ...................................................................................................................................................................... b = ............................................... because .................................................................................................. ...................................................................................................................................................................... [4]
16 NOT TO SCALE M B O A The diagram shows a circle, centre O. AB is a chord of length 12 cm. M is the mid-point of AB and OM = 4.5 cm. Calculate the radius of the circle. .......................................... cm [3]
16 NOT TO SCALE 56° x° y° B M A L C N The diagram shows an isosceles triangle ABC with AB = AC. LCM and BCN are straight lines and LCM is parallel to AB. Angle ACL = 56°. Find the value of x and the value of y. x = ................................................ y = ................................................ [4]
18 In this question, use a straight edge and compasses only and show all your construction arcs. (a) Construct the perpendicular bisector of PQ. P Q [2] (b) Construct the bisector of angle ABC. A B C [2]
19 N L M 19 cm 14 cm 16 cm NOT TO SCALE Calculate angle LMN. Angle LMN = ............................................... [4]
19 The diagram shows a pentagon ABCDE. A B E 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]
20 47° 85° w° y° x° C D E A B NOT TO SCALE The points A, B, C, D and E lie on the circumference of the circle. Angle DCE = 47° and angle CEA = 85°. Find the values of w, x and y. w = ................................................ x = ................................................ y = ................................................ [3]
23 NOT TO SCALE 4 cm 6 cm C P Q B D A 12 cm The diagram shows a triangular prism. AB = 12 cm, BC = 6 cm, PC = 4 cm, angle BCP = 90° and angle QDC = 90°. Calculate the angle between AP and the rectangular base ABCD. ................................................. [4]
25 (a) A Q P B C NOT TO SCALE In the diagram, PQ is parallel to BC. APB and AQC are straight lines. PQ = 8 cm, BC = 10 cm and AB = 9 cm. Calculate PB. PB = .......................................... cm [2] (b) 13 cm NOT TO SCALE 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 [3]
1 Marianne sells photos. (a) The selling price of each photo is $6. (i) The selling price for each photo is made up of two parts, printing cost and profit. For each photo, the ratio printing cost : profit = 5 : 3. Calculate the profit she makes on each photo. $ ............................................... [2] (ii) Calculate her profit as a percentage of the selling price. ............................................% [1] (iii) Calculate the selling price of a photo in euros (€) when the exchange rate is €1 = $1.091 . € ............................................... [2] (b) 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 [3] (c) In a sale, Marianne buys a new camera for $483. This is a reduction of 8% on the original price. Calculate the original price of the camera. $ ............................................... [3]