You can name shapes by their sides and corners. A quadrilateral is any shape with 4 straight sides. Some quadrilaterals have special names, and the names come from their attributes: equal sides and right angles (square corners).
| Name | It must have |
|---|---|
| quadrilateral | 4 straight sides |
| rectangle | 4 sides and 4 right angles |
| rhombus | 4 sides, all the same length |
| square | 4 right angles and 4 equal sides |
Why it works
A name is a promise about attributes. "Rectangle" promises 4 right angles, and nothing about the sides. A square has 4 right angles, so it keeps that promise: every square is a rectangle. A square also has 4 equal sides, so every square is a rhombus too. But a rectangle with two long sides and two short sides is not a square.
Key idea
Check the attributes, not the look. Squares are rectangles and rhombuses, and all of them are quadrilaterals. Some quadrilaterals are none of these: their sides are not all equal and their corners are not all right angles.
Worked example: Is a square a rectangle?
Is every square a rectangle?
- A rectangle needs 4 right angles.
- Every square has 4 right angles.
Answer: Yes
Worked example: Name it
A shape has 4 equal sides but its corners are not right angles. What is it?
- 4 equal sides: a rhombus.
- No right angles, so it is not a square or a rectangle.
Answer: a rhombus
Common mistake
Saying a square is not a rectangle because it "looks different." Shapes are sorted by attributes. Check: does it have 4 right angles? A square does, so it is a rectangle, a special one with equal sides. Also, a square turned on its corner is still a square.