Two-dimensional shapes have attributes: sides (edges), vertices (corners), and angles. Triangles have 3 sides; rectangles have 4 sides with right angles; circles have no sides or corners. Shapes can be sorted by these attributes.
Every two-dimensional shape has a set of measurable, countable properties called attributes. The three most important attributes are sides (the straight line segments that form the boundary of the shape), vertices (the corner points where two sides meet), and angles (the amount of turn at each vertex). You already know how to name and recognize basic shapes — now the goal is to describe *why* a triangle is a triangle and *why* a rectangle is a rectangle using these precise attributes.
Counting sides and vertices is the most reliable way to classify a shape. A triangle always has exactly 3 sides and 3 vertices. A quadrilateral always has 4 sides and 4 vertices — rectangles, squares, and rhombuses are all quadrilaterals because they all share this count. Pentagons have 5, hexagons have 6. Notice a pattern: for straight-sided shapes, the number of sides always equals the number of vertices. If you count 5 corners on a shape, you will always find 5 sides.
Angles add a deeper layer of description. A right angle looks like the corner of a piece of paper — it is a perfect 90-degree turn. Rectangles are special quadrilaterals because *all four* of their angles are right angles. A square is even more special: it has four right angles *and* all four sides equal. Triangles can have right angles too, but they cannot have more than one (three right angles would require more than 180 degrees total, which a triangle cannot have). Circles are the exception to all of this: they have no sides, no vertices, and no angles — just one continuous curved boundary.
Sorting shapes by attributes is a powerful reasoning tool. Instead of memorizing that "this looks like a rectangle," you can check: Does it have 4 sides? Yes. Does it have 4 right angles? Yes. Then it is a rectangle, no matter how it is rotated or what size it is. Two shapes can share some attributes but not others — a square and a non-square rectangle both have 4 right angles, but only the square has all sides equal. Learning to ask "what do these shapes have in common?" and "how are they different?" is the beginning of geometric reasoning.