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Year 8 Maths • AC9M8SP02 • Authored homework

Quadrilateral properties and proof

Practise Quadrilateral properties and proof through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.

10
Short-answer questions
10
Long-answer questions
1
Research/application task

Part A

Short-answer questions

  1. State two properties of a parallelogram.

  2. Find the missing angle in a quadrilateral with angles 95°, 80° and 110°.

  3. Explain why a rectangle is also a parallelogram.

  4. A student says every rhombus is a square. Correct the statement.

  5. Write the rule or formula most useful for Quadrilateral properties and proof.

  6. Show how to check one answer using estimation, substitution or inverse operations.

  7. Write one common mistake students make in Quadrilateral properties and proof and correct it.

  8. Create a small table, diagram or equation that represents this topic.

  9. State where units, exact form or rounding matter in this topic.

  10. Write one exam-style short question on Quadrilateral properties and proof and solve it.

Part B

Long-answer questions

  1. Use congruent triangles to justify why opposite sides of a parallelogram are equal.

  2. Compare a kite, rhombus, rectangle and trapezium using sides, angles and diagonals.

  3. Solve a multi-step problem involving Quadrilateral properties and proof and explain every step clearly.

  4. Create a realistic word problem for Quadrilateral properties and proof, solve it and interpret the answer.

  5. Compare two methods for a problem in Quadrilateral properties and proof and explain which is more efficient.

  6. Write a worked solution that includes a check for reasonableness.

  7. Create a problem with a deliberate trap, then solve it correctly and explain the trap.

  8. Use a diagram, table, graph or equation to model a situation involving Quadrilateral properties and proof.

  9. Explain how this topic connects to a previous Year 7 or Year 8 maths skill.

  10. Write a full-mark response to a challenging Quadrilateral properties and proof question, including reasoning and final answer.

Part C

Research and understanding task

Research a real structure that uses quadrilaterals. Identify the quadrilaterals and explain useful properties.