Looking closely at shapes
To describe and classify shapes, mathematicians look at their attributes: the features you can count or measure.
| Attribute | Question |
|---|---|
| Sides | How many? Straight or curved? Equal lengths? |
| Vertices | How many corners? |
| Angles | Any right angles? Acute or obtuse? |
| Parallel sides | Are any sides always the same distance apart? |
| Symmetry | Can it be folded so both halves match? |
Polygons
A polygon is a closed shape with straight sides. Circles aren’t polygons (curved). An open shape like a "V" isn’t a polygon (not closed).
| Sides | Name |
|---|---|
| 3 | triangle |
| 4 | quadrilateral |
| 5 | pentagon |
| 6 | hexagon |
| 8 | octagon |
| 10 | decagon |
Regular and irregular
A regular polygon has all sides equal and all angles equal. A stop sign is a regular octagon. An irregular polygon doesn’t have all sides and angles equal, but it still has the same name if it has the same number of sides.
Classifying quadrilaterals
| Shape | Key attributes |
|---|---|
| Square | 4 equal sides, 4 right angles |
| Rectangle | opposite sides equal, 4 right angles |
| Rhombus | 4 equal sides, opposite sides parallel |
| Parallelogram | 2 pairs of parallel sides |
| Trapezoid | at least 1 pair of parallel sides |
| Kite | 2 pairs of equal sides next to each other |
Shapes can belong to more than one group. A square is also a rectangle, a rhombus and a parallelogram, because it has all their attributes.
Classifying triangles
- By sides: equilateral (3 equal), isosceles (2 equal), scalene (none equal).
- By angles: right (one 90° angle), acute (all less than 90°), obtuse (one more than 90°).
Sorting tools
A Venn diagram sorts shapes that share attributes, such as "has a right angle" and "has 4 sides". A square goes in the overlap; a right triangle goes only in the right-angle circle.
Worked examples
Example 1: A shape has 4 equal sides but no right angles. Name it.
A rhombus.
Example 2: Is a regular hexagon’s every angle equal?
Yes: regular means equal sides and equal angles.
Example 3: Why is a rectangle a parallelogram?
It has 2 pairs of parallel sides.
Common mistakes
- Thinking shapes can only have one name. A square is a special rectangle.
- Judging by how the shape is turned. A tilted square is still a square.
- Calling any 6-sided shape "not a hexagon" because it’s irregular.
Try it yourself
- What do you call a polygon with 5 sides?
- Name a quadrilateral with exactly one pair of parallel sides.
- Is a circle a polygon? Why?
- Name the triangle with no equal sides.
Answers: 1) pentagon 2) trapezoid 3) No: it has a curved edge. 4) scalene
Quick recap
- Shapes are classified by attributes: sides, angles, parallel sides, symmetry.
- A polygon has straight sides and is closed; a regular polygon has equal sides and angles.
- A shape can belong to several groups.