Quadrilaterals, tiling and the eight directions · Usually met around P4
How quadrilaterals are related
A square is a rectangle and a rhombus.
How to do it
Method
A square is a rectangle and a rhombus
Square → rectangle, rhombus → parallelogram
Another way
Rings inside rings
Quadrilaterals ⊃ parallelograms ⊃ rectangles, rhombuses
In full
A four-sided shape with both pairs of opposite sides parallel is a parallelogram; rectangles (four right angles) and rhombuses (four equal sides) are both parallelograms. A square has four right angles, so it is a rectangle; its four sides are equal, so it is a rhombus too. A trapezium has only one pair of parallel sides, so it isn't a parallelogram. To sort a shape, check in turn: are opposite sides parallel? Are there right angles? Are all four sides equal? Or draw rings inside rings: quadrilaterals hold the parallelograms, which hold the rectangles and the rhombuses, and the squares sit where those two overlap.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A square with sides of 4 cm can also be called which of these?
- A. A trapezium
- B. A rhombus
- C. A pentagon
- D. A triangle
Choose the right answer
Show the answer and working
Answer: B. A rhombus
A square's four sides are equal, so it is a rhombus too.
Example 2
How many of the shapes in the picture are parallelograms?
Show the answer and working
Answer: 4
Only shapes with both pairs of opposite sides parallel count: squares, rectangles and rhombuses do, trapeziums don't. 4 in all.
Example 3
Which sentence is true?
- A. Every square is a rectangle
- B. Every rhombus is a square
- C. Every rectangle is a square
- D. Every parallelogram is a rectangle
Choose the right answer
Show the answer and working
Answer: A. Every square is a rectangle
A square has four right angles and parallel opposite sides, so it is always a rectangle; not the other way round.
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