Year 8 constructions and congruence test to download as PDF

This Year 8 constructions and congruence test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 12-13, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Can the triangle exist?
Answer each part and explain your answer.
1. Can a triangle have sides 5 cm, 7 cm and 13 cm? (2 marks)
2. Can a triangle have sides 6 cm, 8 cm and 10 cm? (1 mark)
3. Is it a right-angled triangle? Show your working. (1 mark)
Question 2 – Constructions
Use a ruler and compasses. Leave your construction arcs.
1. Construct the perpendicular bisector of a line \(AB\) of length 9 cm. (2 marks)
2. Construct a triangle with sides 6 cm, 7 cm and 8 cm. (2 marks)
Question 3 – Congruent triangles
Triangles \(ABC\) and \(PQR\) are congruent, with \(A\) matching \(P\), \(B\) matching \(Q\) and \(C\) matching \(R\). \(AB=9\) cm, \(PR=12\) cm and angle \(P=48^\circ\).
1. Write down the length of \(PQ\). (1 mark)
2. Write down the length of \(AC\). (1 mark)
3. Write down angle \(A\). (1 mark)
4. Name a test that could prove the triangles congruent if two sides and an angle are known. Say which angle is needed. (1 mark)
Question 4 – Problem: the playground
Two paths in a park meet at a point \(O\) at an angle of \(80^\circ\). The council wants to put a bench the same distance from both paths.
1. On which line must the bench be placed? (1 mark)
2. Construct this line. (2 marks)
3. What angle does it make with each path? (1 mark)
Question 5 – Problem: the sail
A sail is made from an isosceles triangle of cloth. The two equal sides are each 5 m. The base is 6 m. A seam is sewn from the apex to the midpoint of the base.
1. Explain why the seam splits the sail into two congruent triangles. (2 marks)
2. Find the length of the seam using Pythagoras. (1 mark)
3. Find the area of the whole sail. (1 mark)

How to use this Year 8 constructions and congruence test

First, revise with the constructions and congruence lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the constructions and congruence test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 8 constructions and congruence test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.