Congruent Triangles – Higher – GCSE Questions These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clone questions using different numbers. The worksheets are provided in a variety of sizes.

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GCSE GCSE GCSE GCSE Edexcel Higher: May 2017 Paper 1, 21 ABCD is a quadrilateral. 1 ABCD is a quadrilateral. D C D C DA = CB Angle DAB = angle ABC Prove that AC = DB. A B DA = CB Angle DAB = angle ABC Prove that AC = DB. A B (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks) GCSE GCSE Edexcel Higher: May 2017 Paper 1, 21 Edexcel Higher: May 2017 Paper 1, 21 1 ABCD is a quadrilateral. 1 ABCD is a quadrilateral. D C D C DA = CB Angle DAB = angle ABC Prove that AC = DB. A B DA = CB Angle DAB = angle ABC Prove that AC = DB. A B (Total for Question 1 is 4 marks) (Total for Question 1 is 4 marks)

GCSE GCSE Edexcel Higher: June 2018 Paper 3, Q21 B S 1 A B S T C D T C D ABCD is a parallelogram. ABS and TCD are straight lines. Angle TBD = angle ACS = 90° (a) Prove that triangle TBD is congruent to triangle ACS. ABCD is a parallelogram. ABS and TCD are straight lines. Angle TBD = angle ACS = 90° (a) Prove that triangle TBD is congruent to triangle ACS. (3) (3) (b) Explain why AT is parallel to SD. (b) Explain why AT is parallel to SD. (2) (2) (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: May 2017 Paper 1, 21 ABCD is a quadrilateral. D C DA = CB Angle DAB = angle ABC Prove that AC = DB. A B (Total for Question 1 is 4 marks)

GCSE Edexcel Higher: June 2018 Paper 3, Q21 1 A B S T C D ABCD is a parallelogram. ABS and TCD are straight lines. Angle TBD = angle ACS = 90° (a) Prove that triangle TBD is congruent to triangle ACS. (3) (b) Explain why AT is parallel to SD. (2) (Total for Question 1 is 5 marks)

GCSE Prove 2 triangles DAB, ABC are congruent. Angle DAB = angle ABC Edexcel Higher: May 2017 Paper 1, 21 1 ABCD is a quadrilateral. D C DA = CB Angle DAB = angle ABC Prove that AC = DB. A B Prove 2 triangles DAB, ABC are congruent. Angle DAB = angle ABC (ANGLE) DA = CB (SIDE) AB is shared by both triangles. (SIDE) Both triangles are congruent (SAS). So, AC must = DB (Total for Question 1 is 4 marks)

GCSE Angle TBD = Angle ACS (given) Edexcel Higher: June 2018 Paper 3, Q21 1 A B S T C D ABCD is a parallelogram. ABS and TCD are straight lines. Angle TBD = angle ACS = 90° (a) Prove that triangle TBD is congruent to triangle ACS. Angle TBD = Angle ACS (given) AC = BD (opposite sides of parallelogram are equal) Angle TDB = Angle SAC (opposite angles of a parallelogram are equal) Therefore, triangles have angle-side-angle the same, ASA: they are congruent (3) (b) Explain why AT is parallel to SD. TBD is congruent to ACS, so AS = TD AS & TD are parallel ASDT is therefore a parallelogram. Opposite sides of a parallelogram are parallel. (2) (Total for Question 1 is 5 marks)

tom@goteachmaths.co.uk Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk