2D Shape Properties
Classify and describe quadrilaterals, triangles, and other polygons using their properties — sides, angles, symmetry, and parallel lines.
Polygons
A polygon is a flat, closed shape with straight sides. Polygons are named by the number of sides they have. A regular polygon has all sides equal and all angles equal. An irregular polygon has sides or angles that are not all equal.
Triangle
3 sides
Quadrilateral
4 sides
Pentagon
5 sides
Hexagon
6 sides
Octagon
8 sides
Circle
Not a polygon
Types of Triangles
Triangles can be classified by their sides or their angles.
Classified by Sides
Equilateral
All 3 sides equal. All angles = 60°.
Isosceles
2 sides equal. 2 base angles equal.
Scalene
No sides equal. No angles equal.
Classified by Angles
Right-angled
Has one 90° angle (shown with a small square).
Acute
All three angles are less than 90°.
Obtuse
One angle is greater than 90°.
Types of Quadrilaterals
A quadrilateral is any shape with exactly 4 sides and 4 angles. The angles of any quadrilateral always add up to 360°.
Square
4 equal sides. 4 right angles. 4 lines of symmetry.
Rectangle
Opposite sides equal. 4 right angles. 2 lines of symmetry.
Rhombus
4 equal sides. Opposite angles equal. 2 lines of symmetry.
Parallelogram
2 pairs of parallel sides. Opposite sides and angles equal.
Trapezium
Exactly 1 pair of parallel sides.
Kite
2 pairs of adjacent equal sides. 1 line of symmetry.
Key Vocabulary
Polygon
A flat, closed 2D shape with straight sides. Triangles, squares, and hexagons are all polygons.
Quadrilateral
Any shape with four straight sides and four angles. All quadrilaterals have angle sum of 360°.
Parallel
Lines that are always the same distance apart and never meet. Shown with arrow marks (→) on diagrams.
Regular Polygon
A polygon where all sides are equal and all angles are equal. E.g. a regular hexagon.
Worked Examples
A shape has 4 equal sides but no right angles. What is it?
Step 1: 4 sides = quadrilateral.
Step 2: All sides equal, but NOT a square (no right angles).
Answer: It is a Rhombus.
A triangle has sides of 5 cm, 5 cm and 8 cm. Classify it.
Step 1: Two sides are equal (5 cm and 5 cm).
Step 2: This means two base angles are also equal.
Answer: It is an Isosceles triangle.
How many lines of symmetry does a regular hexagon have?
Think: A regular hexagon has 6 equal sides. For each side there is a matching line of symmetry.
3 lines pass through opposite vertices, and 3 lines pass through midpoints of opposite sides.
Answer: A regular hexagon has 6 lines of symmetry.
Knowledge Check
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Key Concepts Summary
- ●A polygon is a flat, closed shape with straight sides, named by the number of sides.
- ●Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
- ●A quadrilateral has 4 sides. All quadrilateral angles sum to 360°.
- ●Key quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium, kite.
- ●A regular polygon has all sides equal and all angles equal.