Year 7 Geometry Notes

Geometry is the branch of mathematics that deals with the properties and relationships of points, lines, angles, surfaces, and shapes.

Point: An exact location in space, usually represented by a dot.
Line: A straight one-dimensional figure that has no thickness and extends infinitely in both directions.
Line Segment: A part of a line that is bounded by two distinct endpoints.
Ray: A part of a line that begins at a point and extends infinitely in one direction.

Angle: Formed by two rays with a common endpoint called the vertex.
Types of Angles:
- Acute Angle: Less than 90°.
- Right Angle: Exactly 90°.
- Obtuse Angle: Greater than 90° but less than 180°.
- Straight Angle: Exactly 180°.

2D Shapes: Flat shapes that have length and width but no depth.
- Triangles: Three-sided polygon.
  - Types: Equilateral, Isosceles, Scalene.
- Quadrilaterals: Four-sided polygon.
  - Types: Square, Rectangle, Parallelogram, Trapezoid.
- Circles: A round shape where all points are equidistant from the center.
3D Shapes: Objects that have length, width, and height.
- Cuboid: A three-dimensional shape with height, width, and depth.
- Sphere: A perfectly round three-dimensional shape.
- Cylinder: A three-dimensional shape with two parallel circular bases connected by a curved surface.

Perimeter: The distance around a shape.
- To find the perimeter of a rectangle: P = 2(length + width).
- To find the perimeter of a triangle: Add the lengths of all sides.
Area: The space within a shape.
- For rectangles: Area = length × width.
- For triangles: Area = (base × height) / 2.
- For circles: Area = π × radius².

Volume: The amount of space a three-dimensional shape occupies.
- Volume of a cuboid: Volume = length × width × height.
- Volume of a cylinder: Volume = π × radius² × height.

Understanding geometry is essential as it is used in various real-life applications such as architecture, engineering, and art.