Describe features of 2D shapes
In Year 3 (NSW Stage 2, outcome MA2-2DS-01), students describe the features of 2D shapes: the number of sides and vertices, any right angles, and which sides are equal or parallel.
Students read the marks used on shape diagrams (tick marks for equal sides, arrows for parallel sides and small squares for right angles) and use them to describe triangles, squares, rectangles, rhombuses, kites, trapeziums and other polygons. They compare shapes by their features, name a shape from a description, and explain why a circle has no sides and no corners.
Theory
Describing features of 2D shapes is a Year 3 geometry skill: naming a flat shape by its sides, its vertices (corners) and its angles. This page explains how to count sides and vertices, spot right angles, and tell which sides are equal or parallel for shapes like triangles, squares, rectangles and circles.
A 2D shape is a flat shape. We describe it by looking at its parts. A side is one straight edge. A vertex is a corner, where two sides meet. The word for more than one vertex is vertices.
A shape always has the same number of sides as vertices. A triangle has \(3\) sides and \(3\) vertices. A square has \(4\) sides and \(4\) vertices.
A right angle is a square corner, like the corner of a page. We mark it with a small square. Some sides are special too: equal sides are the same length (shown with matching tick marks), and parallel sides stay the same distance apart and never meet (shown with matching arrows).
A circle is different from these shapes. It has one smooth curved edge, so it has no straight sides and no corners.
2D shapes do not need formulas, but these features are worth remembering. For any straight-sided shape:
| Shape | Sides | Vertices | Right angles |
|---|---|---|---|
| Triangle | 3 | 3 | 0 or 1 |
| Square | 4 | 4 | 4 |
| Rectangle | 4 | 4 | 4 |
| Pentagon | 5 | 5 | It depends (a regular one has 0) |
| Hexagon | 6 | 6 | It depends (a regular one has 0) |
| Circle | 0 (curved) | 0 | 0 |
How to describe a 2D shape
- Count the sides. Trace all the way around the shape and count each straight edge.
- Count the vertices. Count the corners where two sides meet. This number matches the number of sides.
- Check the angles. Look for any square corners. Mark each right angle with a small square.
- Look at the sides. Are any sides equal in length? Are any sides parallel? Use tick marks and arrows to show them.
How to compare two shapes
- Describe each shape. Write its sides, vertices, right angles, equal sides and parallel sides.
- Look for what is the same. For example, a square and a rhombus both have 4 equal sides.
- Look for what is different. For example, a square has 4 right angles but a rhombus does not have to.
It has \(4\) straight sides and \(4\) vertices.
The two small squares show \(2\) right angles.
The matching arrows show that the top and bottom sides are parallel, so it has \(1\) pair of parallel sides.
The single arrows show the top and bottom are parallel. The double arrows show the two slanted sides are parallel. That is \(2\) pairs of parallel sides.
The ticks show opposite sides are equal in length.
There are no small squares, so it has no right angles.
The two slanted sides each have one tick, so \(2\) sides are equal. The bottom side is a different length.
The three sides all lean different ways and every pair meets at a corner, so the triangle has no parallel sides.
\(4\) sides and \(4\) right angles \(\to\) a square or a rectangle.
The sides are not all equal, so it is not a square.
The shape is a rectangle.
Common pitfalls
Frequently asked questions
What is a side of a 2D shape?
A side is one straight edge of a shape. To count the sides, trace all the way around the shape and count each straight edge once.
What is a vertex?
A vertex is a corner, where two sides meet. The word for more than one vertex is vertices. A shape always has the same number of vertices as sides.
What is a right angle?
A right angle is a square corner, like the corner of a page or a book. We mark a right angle with a small square. A right-angled triangle has one right angle.
What are parallel sides?
Parallel sides stay the same distance apart all the way along and never meet, like the two rails of a train track. We show parallel sides with matching arrows.
How is a square different from a rectangle?
Both have \(4\) sides and \(4\) right angles. A square has all \(4\) sides equal in length, while a rectangle only has its opposite sides equal.
Is the edge of a circle a side?
No. A side must be straight, and the edge of a circle is one smooth curve. That is why a circle has no sides and no corners.