EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Congruence
Congruence · Similarity and congruence · Lesson 1 of 5 · 15 marks · 25 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Give reasons for your answers.
Question 1 GIVE A REASON (3 marks)
The diagram shows three triangles A, B and C. Two of the triangles are congruent. Write down which two, and give a reason.
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(Total for Question 1 = 3 marks)
Question 2 SHOW THAT (3 marks)
Triangle ABC has AB = 5 cm, BC = 7 cm and angle ABC = 50°. Triangle PQR has PQ = 5 cm, QR = 7 cm and angle PQR = 50°. Show that triangle ABC is congruent to triangle PQR.
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(Total for Question 2 = 3 marks)
Question 3 GIVE A REASON (2 marks)
Two triangles both have angles of 40°, 60° and 80°. Ben says they must be congruent. Explain why Ben is not necessarily correct.
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(Total for Question 3 = 2 marks)
Question 4 WORK OUT (2 marks)
Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 6 cm, BC = 8 cm and DF = 10 cm. Write down the length of AC.
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(Total for Question 4 = 2 marks)
Question 5 EXPLAIN (3 marks)
Triangle ABC is right-angled at B, with hypotenuse AC = 10 cm and AB = 6 cm. Triangle PQR is right-angled at Q, with hypotenuse PR = 10 cm and PQ = 6 cm. Explain why the triangles are congruent.
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(Total for Question 5 = 3 marks)
Question 6 DECIDE (2 marks)
Triangle ABC has sides 4 cm, 5 cm and 6 cm. Triangle DEF has sides 6 cm, 4 cm and 5 cm. Are the triangles congruent? Give a reason.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 15 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
Triangles A and B are congruent by SAS: two sides (6 cm and 8 cm) and the included angle 50° are equal.
• A and B B1
• Two sides and the included angle equal M1
• SAS A1
Question 2 (3 marks)
AB = PQ = 5 cm, BC = QR = 7 cm, and angle ABC = angle PQR = 50°. Two sides and the included angle are equal, so the triangles are congruent by SAS.
• Equal sides stated M1
• Equal included angle stated M1
• SAS and conclusion A1
Question 3 (2 marks)
Equal angles (AAA) do not prove congruence. The triangles could be different sizes, so they are similar but not necessarily congruent.
• AAA is not a congruence condition M1
• The triangles could be different sizes C1
Question 4 (2 marks)
AC = DF = 10 cm, because AC and DF are corresponding sides.
• Corresponding sides identified M1
• 10 A1
Question 5 (3 marks)
Each triangle has a right angle, a hypotenuse of 10 cm and another side of 6 cm. This is RHS, so the triangles are congruent.
• Right angle in each B1
• Hypotenuse and one other side equal M1
• RHS A1
Question 6 (2 marks)
Yes, all three sides are equal (SSS).
• Yes B1
• SSS B1