Geometry: Basic Ideas

Why is a Square also a Rectangle?

by Bonnie Yoder

• You know how a puppy is a kind of dog, but not all dogs are puppies? Well, the same thing is true for lots of other categories of things, including squares and rectangles.
  • Other Examples:
    • All lollipops are candies, but not all candies are lollipops.
    • All girls are people, but not all people are girls.
    • All cars are machines, but not all machines are cars.
• Puppies, lollipops, girls and cars are all examples of specific types of a more general category, like dogs, candy, people and machines. All the specific examples, puppies, lollipops, girls and cars, have more characteristics that make them more specific.
  • You can often make up your own special characteristics that a certain category must have in order to be considered something more specific.
    • For a dog to be a puppy it has to be a very young dog.
    • For a candy to be a lollipop, it must be on a stick.
• All of this is true of geometric shapes too! The next example is presented as a display of how a square is a special kind of rectangle.