You have seen the family tree of shapes. The tree is useful because properties pass down it: whatever is true of every shape in a family is true of every shape in its smaller families too.
Idea clave
If every rectangle has a property, then every square has it, because every square is a rectangle. Properties pass down the tree, never up: a square's 4 equal sides do not pass up to all rectangles.
Por qué funciona
“Every rectangle has 4 right angles” is a statement about all rectangles, and squares are among them. So a square must have 4 right angles. It also inherits from parallelograms: opposite sides parallel and equal, opposite angles equal. A square gets its equal sides from the rhombus family.
Worked examples
Ejemplo resuelto: What a square inherits
Squares are rectangles. What must every square have because of that?
- Every rectangle has 4 right angles.
- So every square has 4 right angles. (Its 4 equal sides come from being a rhombus.)
Respuesta: 4 right angles
Ejemplo resuelto: Is a square a rectangle?
Is every square a rectangle? Is every rectangle a square?
- A rectangle only needs 4 right angles. Every square has them, so every square is a rectangle.
- A square also needs 4 equal sides. Many rectangles do not have them.
Respuesta: Yes; no
Error común
Saying a square cannot be a rectangle, or that a rectangle must have two long and two short sides. The rule for a rectangle says nothing about side lengths. Check against the rule itself, not against the picture you usually see.