Geometrical Terms (Copy)
Geometry Vocabulary Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Geometrical Terms, Triangles, Quadrilaterals, Polygons, Solids
1. Basic Geometrical Terms
- Point: A location in space.
- Vertex: A corner where two sides meet.
- Line: A straight one-dimensional figure with no thickness, extends infinitely.
- Parallel Lines: Lines that never meet and stay the same distance apart.
- Perpendicular Lines: Lines that meet at a right angle (90°).
- Bearing: A direction measured clockwise from north (0° to 360°).
- Right Angle: Exactly 90°.
- Acute Angle: Less than 90°.
- Obtuse Angle: More than 90° but less than 180°.
- Reflex Angle: More than 180° but less than 360°.
- Interior Angles: Angles inside a polygon.
- Exterior Angles: Angles formed outside a polygon when sides are extended.
- Similar Figures: Same shape but different size (angles equal, sides proportional).
- Congruent Figures: Same shape and same size (identical in every way).
- Scale Factor: The ratio of lengths between two similar figures.
2. Vocabulary of Triangles
| Type of Triangle | Description |
|---|---|
| Equilateral | All sides and angles are equal (each angle = 60°). |
| Isosceles | Two sides and two angles are equal. |
| Scalene | No sides or angles are equal. |
| Right-Angled | One angle is exactly 90°. |
3. Vocabulary of Special Quadrilaterals
| Quadrilateral | Properties |
|---|---|
| Square | All sides equal, all angles 90°, opposite sides parallel. |
| Rectangle | Opposite sides equal, all angles 90°. |
| Kite | Two pairs of adjacent sides equal, one pair of opposite angles equal. |
| Rhombus | All sides equal, opposite sides parallel, opposite angles equal. |
| Parallelogram | Opposite sides equal and parallel, opposite angles equal. |
| Trapezium | Only one pair of opposite sides parallel. |
4. Vocabulary of Polygons
| Polygon | Number of Sides | Notes |
|---|---|---|
| Regular Polygon | All sides and all angles are equal. | |
| Irregular Polygon | Sides and/or angles are not all equal. | |
| Pentagon | 5 sides. | |
| Hexagon | 6 sides. | |
| Octagon | 8 sides. | |
| Decagon | 10 sides. |
5. Solids and Nets
- Net: A two-dimensional shape that can be folded to form a 3D solid.
- Simple Solids:
- Cube
- Cuboid (rectangular box)
- Cylinder
- Cone
- Sphere
- Pyramid (square-based, triangular-based)
6. Important Facts
- Sum of Interior Angles of a Polygon = (n – 2) × 180°, where n = number of sides.
- Exterior Angle of a Regular Polygon = 360° ÷ number of sides.
- Parallel lines never meet no matter how far they are extended.
- Perpendicular lines always meet at a right angle.
This covers all required CORE-level geometry vocabulary and simple interpretation skills without needing proofs or complex constructions.
Circle Vocabulary and Simple Solids Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Circle Terms and Solids Vocabulary
1. Vocabulary of a Circle
| Term | Definition |
|---|---|
| Centre | The exact middle point of a circle. |
| Radius | A straight line from the centre to any point on the circle. |
| Radii | Plural of radius (more than one radius). |
| Diameter | A straight line passing through the centre, connecting two points on the circle. Diameter = 2 × radius. |
| Circumference | The distance around the edge (perimeter) of the circle. |
| Semicircle | Half of a circle. |
| Chord | A straight line joining two points on the circle (does not have to pass through the centre). |
| Tangent | A straight line that touches the circle at exactly one point. |
| Arc | A part of the circumference of a circle. |
| Sector | A region enclosed by two radii and an arc (looks like a slice of pizza). |
| Segment | A region between a chord and the arc above it. |
2. Vocabulary of Simple Solids
| Solid | Definition |
|---|---|
| Cube | A solid with six equal square faces. |
| Cuboid | A solid with six rectangular faces (like a box). |
| Prism | A solid with two identical, parallel faces and rectangular sides connecting them. |
| Cylinder | A solid with two parallel, identical circular faces and a curved surface joining them. |
| Pyramid | A solid with a polygon base and triangular faces meeting at a single point (the apex). |
| Cone | A solid with a circular base and a curved surface narrowing to a point (the apex). |
| Sphere | A perfectly round solid ball, like a basketball. |
3. Parts of Solids
| Term | Definition |
|---|---|
| Face | A flat or curved surface on a solid. |
| Surface | The outside boundary or area of a solid. |
| Edge | A straight line where two faces meet. |
4. Important Notes
- Diameter = 2 × Radius.
- Circumference ≈ π × Diameter or 2π × Radius.
- A tangent always meets a circle at exactly one point and is perpendicular to the radius at the point of contact.
- In a prism or cylinder, the two ends (bases) are parallel and identical.
- In a pyramid or cone, the base is connected to an apex.
This covers all CORE-level vocabulary related to circles and simple three-dimensional solids without requiring proofs or advanced properties.