These questions ask which properties a named quadrilateral must have, how its angles or diagonals behave, and which names can describe the same shape. Test every stated condition instead of relying on a familiar appearance.
Build each shape from its conditions
| Shape family | Conditions and useful consequences |
|---|---|
| Parallelogram | It has two pairs of parallel sides. Opposite sides and opposite angles are equal, while adjacent angles total 180 degrees. Beside a 68 degree angle is 112 degrees. |
| Rectangle | It is a parallelogram with four right angles. Opposite sides are equal, and its diagonals are equal in length, but they need not cross at right angles. |
| Rhombus | It is a parallelogram with four equal sides. Its diagonals cross at right angles, but they need not be equal in length, and its corners need not be right angles. |
| Square | It has four equal sides and four right angles, so it is also a rectangle, a rhombus and a parallelogram. A side length of 9 cm gives four matching sides, while every corner remains a right angle. |
| Trapezoid in U.S. usage, trapezium in U.K. usage | Both regional names describe a quadrilateral with a pair of parallel sides. Definitions vary on whether other parallelograms belong to this family, so use only the shared parallel-side fact unless the convention is stated. |
Think of the names as nested conditions. Adding four right angles to a parallelogram produces a rectangle; adding four equal sides produces a rhombus; satisfying both additions produces a square. When the question asks for the most exact name, choose the narrowest family whose full conditions are met. When it asks for every true name, keep every wider family too.
Where property checks go wrong
| Trap | How to reject it |
|---|---|
| Giving every rectangle four equal sides | A rectangle guarantees four right angles and equal opposite sides. Equal neighbouring sides are an extra condition, so test them separately. |
| Assuming every parallelogram has four equal angles | Only opposite angles must match. If all four matched, the full-turn total would make every corner a right angle and the shape would be a rectangle. |
| Turning every rhombus into a square | Four equal sides do not force right angles. Check the corners independently before moving to the narrower square family. |
| Swapping the rectangle and rhombus diagonal facts | A rectangle guarantees equal diagonal lengths. A rhombus guarantees a right-angle crossing. Both facts occur together in a square. |
| Treating shape families as separate boxes | A narrower family keeps the conditions of its wider families. Decide whether the wording asks for the narrowest name or for all names that remain true. |
Try it
Think about how the names square and rectangle relate to each other. Select all the statements below that are true.
- Every square is a rectangle.
- Every rectangle is a square.
- A rectangle whose sides are not all equal is not a square.
- No square may be called a rectangle, since the two names describe different shapes.
One angle of a parallelogram measures 70 degrees. Enter the number of degrees in each angle next to it.
A quadrilateral has four right angles, and every one of its sides measures 8 centimetres. What is the most exact name for this shape?
- rectangle
- parallelogram
- square
- rhombus