Shapes and symmetry
Circles and polygons
A chord and a tangent look similar until you notice one crosses the circle and the other only grazes it.
Parts of a circle you know
CENTRE — the middle point. RADIUS — a line from the centre to the edge. DIAMETER — a line right across, through the centre. CIRCUMFERENCE — the distance all the way round the edge. The diameter is always twice the radius.
Two new parts
A CHORD is a straight line that starts and finishes ON the circumference. A TANGENT is a straight line that touches the circumference at only ONE point. The difference: a chord cuts across the circle and meets it twice; a tangent just grazes it and meets it once. And note: if a chord passes through the centre, it IS the diameter. So the diameter is a special chord — the longest one.
Regular and irregular polygons
A POLYGON is a shape with straight sides. A REGULAR polygon has ALL sides the same length and ALL angles the same size. An IRREGULAR polygon does not. A regular pentagon has five equal sides, five equal angles, five lines of symmetry and order 5 rotational symmetry. The names by number of sides: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.
Worked examples
How is a chord different from a tangent?
- A chord starts and finishes ON the circumference.
- A tangent touches at only one point.
Answer: A chord meets the circle twice, a tangent once
Is the diameter a chord?
- A chord through the centre IS the diameter.
Answer: Yes — the longest chord of all
The radius of a circle of diameter 10 cm
- The diameter is always twice the radius.
- 10 ÷ 2 = 5.
Answer: 5 cm
What makes a polygon regular?
- All sides the same length.
- All angles the same size.
Answer: Both conditions, not just one
A regular pentagon's symmetry
- Five equal sides and five equal angles.
Answer: 5 lines of symmetry and order 5
Naming a polygon with 8 sides
- Count the sides and use the standard name.
Answer: An octagon
Where you see this in real life
- A bicycle wheel's spokes are radii; the tyre is the circumference. A straight road just touching a roundabout is a tangent.
- A stop sign is a regular octagon — eight equal sides, and it reads the same however it is mounted.
Key words
- Chord
- a straight line from one point on the circumference to another
- Tangent
- a straight line touching the circumference at one point only
- Polygon
- a shape with straight sides
- Regular polygon
- a polygon with all sides and angles equal
- Irregular polygon
- a polygon whose sides or angles are not all equal
- Sketch
- a quick drawing that shows the key features
- Circumference
- the distance all the way round a circle
- Radius
- a line from the centre to the edge
- Diameter
- a line right across through the centre