Skip to content
Try on iPad

Geometric proof: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on G6 Geometric proof, 2017–2025, with its mark scheme and examiner’s report.

Find questions921
Exam
All years
Calculator

921 questions

  1. Q12

    June 2025 · Paper 5

    4 marksG5 Congruent trianglesG6 Geometric proof
    The whole paper ↗
    June 2025 Paper 5, question 12: A Not to scale D B C ABC is an equilateral triangle. BD is perpendicular to AC. Prove that triangle ABD is congruent to triangle CBD.

  2. Q15

    November 2023 · Paper 4

    3 marksG5 Congruent trianglesG6 Geometric proof
    The whole paper ↗
    November 2023 Paper 4, question 15: P, Q, T and V are points on the circumference of a circle. TV is a diameter of the circle. M is a point on PQ such that PM = MQ. V Not to scale Q M P T Complete

  3. Q8

    November 2023 · Paper 6

    5 marksG3 Angles and polygonsG6 Geometric proof
    The whole paper ↗
    November 2023 Paper 6, question 8: The diagram shows four triangles that are joined together. A B C D Not to scale F E • Points A, B, C and D lie on a straight line. • Triangles ABF and CDE are e

  4. Q13

    November 2022 · Paper 5

    3 marksG6 Geometric proofG10 Circle theorems
    The whole paper ↗
    November 2022 Paper 5, question 13: Points A, B, C and D lie on the circumference of a circle. Line AC intersects line BD at point E. B Not to scale A E D C Prove that triangle AED is similar to t

  5. Q9

    November 2020 · Paper 5

    4 marksG6 Geometric proof
    The whole paper ↗
    November 2020 Paper 5, question 9: In the diagram, AB and DC are parallel lines of equal length. D C Not to scale A B Prove that angle DAB = angle BCD.

  6. Q11

    November 2019 · Paper 4

    4 marksG5 Congruent trianglesG6 Geometric proof
    The whole paper ↗
    November 2019 Paper 4, question 11: (a) Are these two triangles definitely congruent? Give a reason. Not to scale B E 64° 64° 36° 80° 36° 80° A C D F because (b) Prove that these two triangles are

  7. Q9

    June 2019 · Paper 4

    5 marksG3 Angles and polygonsG6 Geometric proof
    The whole paper ↗
    June 2019 Paper 4, question 9: The diagram shows triangle ABC. CD is parallel to AB. A, C and E lie in a straight line. Angles of size a°, b° and c° are shown. B D b° Not to scale c° a° A C E

  8. Q14

    June 2019 · Paper 5

    3 marksG19 Similar shapesG6 Geometric proof
    The whole paper ↗
    June 2019 Paper 5, question 14: In the diagram AB is parallel to CD. AED and BEC are straight lines. A B E Not to scale C D Prove that triangle ABE is similar to triangle CDE.

  9. Q11

    June 2018 · Paper 6

    4 marksG6 Geometric proofG5 Congruent triangles
    The whole paper ↗
    June 2018 Paper 6, question 11: The diagram below shows two triangles. B 80° Not to scale C 56° A 44° 80° D Prove that triangle ABC is congruent to triangle ACD.

  10. Q12

    June 2018 · Paper 6

    5 marksG6 Geometric proofG19 Similar shapes
    The whole paper ↗
    June 2018 Paper 6, question 12: The diagram below shows two right-angled triangles. R Not to scale 4 cm 8 cm Q S 10 cm P Prove that triangles PQS and QRS are similar.

  11. Q10

    November 2017 · Paper 5

    4 marksG6 Geometric proofG5 Congruent triangles
    The whole paper ↗
    November 2017 Paper 5, question 10: ABCD is a quadrilateral. AD = AB and CD = CB. A Not to scale D B C Prove that angle ADC is equal to angle ABC.

  12. Q13

    June 2017 · Paper 6

    4 marksG6 Geometric proofG5 Congruent triangles
    The whole paper ↗
    June 2017 Paper 6, question 13: A and B are points on the circumference of a circle, centre O. CA and CB are tangents to the circle. A Not to scale C O B Prove that triangle OAC is congruent t
All 12 questions on Geometric proof, as a list
  1. June 2025, Paper 5, Q12 (4 marks): A Not to scale D B C ABC is an equilateral triangle. BD is perpendicular to AC. Prove that triangle ABD is congruent to triangle CBD.
  2. November 2023, Paper 4, Q15 (3 marks): P, Q, T and V are points on the circumference of a circle. TV is a diameter of the circle. M is a point on PQ such that PM = MQ. V Not to scale Q M P T Complete
  3. November 2023, Paper 6, Q8 (5 marks): The diagram shows four triangles that are joined together. A B C D Not to scale F E • Points A, B, C and D lie on a straight line. • Triangles ABF and CDE are e
  4. November 2022, Paper 5, Q13 (3 marks): Points A, B, C and D lie on the circumference of a circle. Line AC intersects line BD at point E. B Not to scale A E D C Prove that triangle AED is similar to t
  5. November 2020, Paper 5, Q9 (4 marks): In the diagram, AB and DC are parallel lines of equal length. D C Not to scale A B Prove that angle DAB = angle BCD.
  6. November 2019, Paper 4, Q11 (4 marks): (a) Are these two triangles definitely congruent? Give a reason. Not to scale B E 64° 64° 36° 80° 36° 80° A C D F because (b) Prove that these two triangles are
  7. June 2019, Paper 4, Q9 (5 marks): The diagram shows triangle ABC. CD is parallel to AB. A, C and E lie in a straight line. Angles of size a°, b° and c° are shown. B D b° Not to scale c° a° A C E
  8. June 2019, Paper 5, Q14 (3 marks): In the diagram AB is parallel to CD. AED and BEC are straight lines. A B E Not to scale C D Prove that triangle ABE is similar to triangle CDE.
  9. June 2018, Paper 6, Q11 (4 marks): The diagram below shows two triangles. B 80° Not to scale C 56° A 44° 80° D Prove that triangle ABC is congruent to triangle ACD.
  10. June 2018, Paper 6, Q12 (5 marks): The diagram below shows two right-angled triangles. R Not to scale 4 cm 8 cm Q S 10 cm P Prove that triangles PQS and QRS are similar.
  11. November 2017, Paper 5, Q10 (4 marks): ABCD is a quadrilateral. AD = AB and CD = CB. A Not to scale D B C Prove that angle ADC is equal to angle ABC.
  12. June 2017, Paper 6, Q13 (4 marks): A and B are points on the circumference of a circle, centre O. CA and CB are tangents to the circle. A Not to scale C O B Prove that triangle OAC is congruent t

Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every OCR GCSE Maths paper.

Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.