Geometry is a branch of mathematics concerned with the properties and relations of points,
lines, surfaces, solids, and higher-dimensional analogs.
Basic Concepts
1. Points and Lines:
o Point: An exact position or location in a space, usually represented by a dot.
o Line: A straight one-dimensional figure having no thickness and extending
infinitely in both directions.
2. Types of Lines:
o Line Segment: A part of a line that is bounded by two distinct end points.
o Ray: A part of a line that starts at one point and extends infinitely in one
direction.
3. Angles:
o Formed by two rays (or line segments) with a common endpoint called the
vertex.
o Types of Angles:
Acute Angle: Less than 90°.
Right Angle: Exactly 90°.
Obtuse Angle: More than 90° but less than 180°.
Straight Angle: Exactly 180°
Plane Geometry
1. Shapes and Properties:
o Triangle: A three-sided polygon.
Types: Equilateral, isosceles, and scalene.
o Quadrilateral: A four-sided polygon.
Types: Square, rectangle, parallelogram, trapezoid.
o Circle: A round shape with all points at the same distance from the center.
2. Formulas:
o Perimeter: The total length of the boundary of a shape.
o Area: The amount of space enclosed within a shape.
Triangle Area: 12×base×height\frac{1}{2} \times \text{base} \times \
text{height}21×base×height
Rectangle Area: length×width\text{length} \times \
text{width}length×width
Circle Area: π×radius2\pi \times \text{radius}^2π×radius2
Solid Geometry
1. 3D Shapes and Properties:
o Cube: Six equal square faces.
o Cuboid: Six rectangular faces.
o Sphere: All points equidistant from the center.
o Cylinder: Two parallel circular bases connected by a curved surface.
2. Formulas:
o Surface Area: The total area covered by the surface of a 3D shape.
Cube Surface Area: 6×side26 \times \text{side}^26×side2
Sphere Surface Area: 4π×radius24 \pi \times \
text{radius}^24π×radius2
o Volume: The amount of space enclosed within a 3D shape.
Cube Volume: side3\text{side}^3side3
Cylinder Volume: π×radius2×height\pi \times \text{radius}^2 \times \
text{height}π×radius2×height
Applications of Geometry
Geometry is used in various fields such as art, architecture, engineering, robotics, astronomy,
and everyday life activities like navigation and construction
