Attributes of Two-Dimensional Shapes

Two-dimensional (2D) shapes are completely flat. We can describe and sort these shapes by looking at their special features, called attributes. The most common attributes are the number of sides, the number of corners, and the lengths of those sides.

Sides and Vertices

• Sides: The straight lines that make up the outside of a shape.
• Vertices (Corners): The points where two sides meet. One corner is called a vertex, and more than one are called vertices.

A great rule to remember is that for any flat shape made of straight lines, the number of sides always equals the number of vertices!

Naming Shapes by Their Attributes

Let's look at some common shapes and how many sides and corners they have:

• Triangle: Has $3$ sides and $3$ vertices.
• Quadrilateral: Any shape with $4$ sides and $4$ vertices.
• Pentagon: Has $5$ sides and $5$ vertices.
• Hexagon: Has $6$ sides and $6$ vertices.

Square vs. Rectangle

Both squares and rectangles are quadrilaterals, meaning they both have $4$ sides and $4$ corners. So, how are they different?

• Square: A square has $4$ sides that are all exactly the same length (equal sides).
• Rectangle: A rectangle has opposite sides that are equal. The top and bottom are the same length, and the left and right sides are the same length.

(Fun fact: Because a square has equal opposite sides, every square is actually a special kind of rectangle!)

Example Questions

• How is a square different from a rectangle? A square must have all $4$ sides equal, while a normal rectangle usually has two long sides and two short sides.
• What do you call a shape with $5$ sides? A pentagon! If you draw any closed flat shape with $5$ straight lines, you have drawn a pentagon.
• Which shapes have all equal sides? A square always has equal sides. Other shapes, like triangles, pentagons, and hexagons, can have all equal sides (these are called "regular" shapes), but they don't have to.