EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Similarity
Similarity · Similarity and congruence · Lesson 3 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. Show your working.
Question 1 WORK OUT (3 marks)
The diagram shows two similar triangles, ABC and DEF. AB = 6 cm, BC = 10 cm, AC = 8 cm and DE = 9 cm. Work out the length of EF.
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(Total for Question 1 = 3 marks)
Question 2 WORK OUT (2 marks)
For the triangles in the last question, work out the length of DF.
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(Total for Question 2 = 2 marks)
Question 3 WORK OUT (3 marks)
Rectangle A is 4 cm by 6 cm. Rectangle B is similar to rectangle A. The shorter side of rectangle B is 10 cm. Work out the length of the longer side of rectangle B.
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(Total for Question 3 = 3 marks)
Question 4 SHOW THAT (3 marks)
In triangle PQR, angle P = 50° and angle Q = 60°. In triangle XYZ, angle X = 50° and angle Z = 70°. Show that triangles PQR and XYZ are similar.
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(Total for Question 4 = 3 marks)
Question 5 EXPLAIN (2 marks)
A photograph is 12 cm by 8 cm. It is enlarged so that its width is 30 cm. Work out the height of the enlarged photograph.
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(Total for Question 5 = 2 marks)
Question 6 DECIDE (2 marks)
Are a 3 cm by 5 cm rectangle and a 9 cm by 14 cm rectangle similar? 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)
The scale factor is 9/6 = 1.5. EF = 10 × 1.5 = 15 cm.
• Scale factor 1.5 M1
• 10 × 1.5 M1
• 15 A1
Question 2 (2 marks)
DF = 8 × 1.5 = 12 cm.
• 8 × 1.5 M1
• 12 A1
Question 3 (3 marks)
The scale factor is 10 ÷ 4 = 2.5. The longer side is 6 × 2.5 = 15 cm.
• Scale factor 2.5 M1
• 6 × 2.5 M1
• 15 A1
Question 4 (3 marks)
Angle R = 180 − 50 − 60 = 70° and angle Y = 180 − 50 − 70 = 60°. Both triangles have angles 50°, 60° and 70°, so they are similar.
• Finding a third angle M1
• Finding the other third angle M1
• All angles equal, so similar C1
Question 5 (2 marks)
The scale factor is 30 ÷ 12 = 2.5. The height is 8 × 2.5 = 20 cm.
• 30 ÷ 12 M1
• 20 A1
Question 6 (2 marks)
9 ÷ 3 = 3 but 14 ÷ 5 = 2.8. The scale factors are different, so the rectangles are not similar.
• Comparing the ratios M1
• Not similar with a reason C1