Geometry — IGCSE Mathematics - International (0607) questions by topic
Shape properties and circle theorems both feature: naming a regular polygon from its perimeter, completing statements about rotational and line symmetry, and finding angles in an isosceles triangle or a cyclic pentagon with a tangent line all test geometric reasoning.
Find, state, work out, name and draw are the leading command words, worth from 1 to 8 marks, across 20 questions set in 2025 papers. Circle theorem and angle questions reward naming the exact rule used, so practise stating which property justifies each step, then use instant marking to check whether a correct angle was reached by a properly named reason or by guesswork.
May–June 2025, Paper 11
Draw all the lines of symmetry on this rectangle.
Answer this question and get it marked →The diagram shows an angle x marked at the vertex where two line segments meet, forming an obtuse angle opening downwards. Measure angle x.
Answer this question and get it marked →Ridwan draws a regular shape with side length 4 cm. The perimeter of the shape is 12 cm. Write down the mathematical name of this shape.
Answer this question and get it marked →The exterior angle of a polygon is 60 degrees. Work out the number of sides of this polygon.
Answer this question and get it marked →May–June 2025, Paper 12
P and Q are points on the circle, centre O. POQ and AQB are straight lines. Write down the mathematical name for PQ.
Answer this question and get it marked →In triangle ABC, AB = AC. BCD is a straight line. Angle ACD = 130°. Find angle BAC. The diagram (not to scale) shows an isosceles triangle ABC with apex A at the top and base BC.…
Answer this question and get it marked →May–June 2025, Paper 21
The diagram shows triangle ABD with point C on the straight line BCD. Lines BA, AD and AC are drawn. The angle ADC at D is marked 68 degrees. In the diagram AC = BC = AD (shown by…
Answer this question and get it marked →A regular pentagon is shown. Draw all the lines of symmetry of this regular pentagon.
Answer this question and get it marked →A, B, C, D, E and F are points on a circle, centre O. Angle FAB = 75 degrees and angle BCD = 113 degrees. Find angle BFE.
Answer this question and get it marked →May–June 2025, Paper 22
A quadrilateral has exactly one pair of parallel sides. Write down the mathematical name of this quadrilateral.
Answer this question and get it marked →The diagram shows a circle, centre O (NOT TO SCALE). AOBP is a straight line. PC is a tangent to the circle. Points A, D, C and B lie on the circle, with D and C on the upper arc.…
Answer this question and get it marked →May–June 2025, Paper 23
A regular polygon has 20 sides. Work out the size of one interior angle of the polygon.
Answer this question and get it marked →A, B, C, D and E lie on the circle. The diagram (not to scale) shows the cyclic pentagon ABCDE inscribed in a circle, with TU a tangent to the circle at C. Angle ABD = 70° (marked…
Answer this question and get it marked →May–June 2025, Paper 31
The diagram shows 4 straight lines. BC and AD are parallel. Write down the mathematical name of the quadrilateral ABCD.
Answer this question and get it marked →The diagram shows an isosceles triangle (not to scale). The apex angle at the top is 66°. The two sides from the apex are marked as equal. At the bottom-right vertex, x° is the…
Answer this question and get it marked →May–June 2025, Paper 32
The diagram shows a regular 5-sided polygon (NOT TO SCALE). Write down the mathematical name for this polygon.
Answer this question and get it marked →The diagram shows a shape made from a square of side 8 cm and four equilateral triangles (NOT TO SCALE). The square is HBDF (with H top-left, B top-right, D bottom-right, F…
Answer this question and get it marked →May–June 2025, Paper 33
X and Y are points on a circle, centre O. Complete each sentence with a mathematical term. OX is a .................... of the circle. XY is a .................... of the circle.
Answer this question and get it marked →May–June 2025, Paper 43
Complete the statements. A rhombus has rotational symmetry of order ........................ A parallelogram has ........................ lines of symmetry.
Answer this question and get it marked →In the diagram, triangle ABC has CA = CB and ABE is a straight line. The angle at the apex C is marked x°. The exterior angle at B (between CB produced beyond the triangle and the…
Answer this question and get it marked →Other IGCSE Mathematics - International topics
- Algebra (75)
- Number (70)
- Statistics (21)
- Mensuration (18)
- Functions (14)
- Trigonometry (14)
- Coordinate geometry (8)
- Vectors and transformations (8)
- Sets (6)
- Probability (5)