Quadrilaterals (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on understanding quadrilaterals and practical geometry for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on understanding quadrilaterals and practical geometry at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Figures are not drawn to scale. Rough work may be done at the side of each page.

Sample questions from this worksheet

A preview of what's inside Quadrilaterals (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The sum of the interior angles of any quadrilateral is _______.

   • A360°correct
   • B270°
   • C180°
   • D540°
   Solution: A quadrilateral can be divided by one diagonal into two triangles, and each triangle has an angle sum of 180°. So the total is 2 × 180° = 360°.

2. 2. The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The largest angle is _______.

   • A144°correct
   • B72°
   • C108°
   • D36°
   Solution: Let the angles be x, 2x, 3x and 4x.
   x + 2x + 3x + 4x = 360°
   10x = 360°, so x = 36°.
   The largest angle is 4x = 4 × 36° = 144°.

3. 3. Consider the following statements.(i) Every square is a rhombus.(ii) Every rhombus is a square.(iii) The diagonals of a rectangle bisect each other and are equal.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(i) and (iii) onlycorrect
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is true — a square has four equal sides, which is exactly the definition of a rhombus. Statement (ii) is false; a rhombus need not have right angles, so it need not be a square. Statement (iii) is true. Hence (i) and (iii).