Stage 8 - Q1 - 2 marks
How many straight sides does every quadrilateral have?
Hint
Use the meaning of quadrilateral.
Stage 8 - Q2 - 2 marks
State one property shared by every rectangle and every square.
Hint
Look for a property that remains true even when a rectangle is not a square.
Stage 8 - Q3 - 2 marks
A non-square rhombus has one angle of 60°. Find all four angles.
Hint
Opposite angles are equal and adjacent angles sum to 180°.
Stage 8 - Q4 - 2 marks
A rectangle is 4 cm by 9 cm. Name three families containing it.
Hint
Use the inclusive trapezium definition.
Stage 8 - Q5 - 3 marks
Give a quadrilateral that is a kite and a parallelogram. Explain.
Hint
Consider a shape with all four sides equal.
Stage 8 - Q6 - 3 marks
A pupil says every trapezium is a parallelogram. Give a counterexample under the inclusive definition.
Hint
The family condition asks for at least one pair, not two.
Stage 8 - Q7 - 3 marks
A quadrilateral has equal opposite sides and one pair of adjacent sides equal. What follows about all four sides?
Hint
Link the adjacent equality with the two opposite-side equalities.
Stage 8 - Q8 - 3 marks
A rectangle has perimeter 28 cm and one side 7 cm. Explain why it is a square.
Hint
Use the perimeter to determine the missing adjacent side.
Stage 8 - Q9 - 3 marks
Can a quadrilateral have exactly three right angles? Explain.
Hint
Subtract the three known right angles from a full turn.
Stage 8 - Q10 - 5 marks
Challenge: a shape is already known to be a parallelogram. Design just two yes/no tests whose four possible outcomes distinguish a square, a non-square rectangle, a non-square rhombus and a general parallelogram.
Hint
Use one side condition and one angle condition, and justify every outcome.