Sandeep Jaiswal's notes define key concepts for lines and angles in geometry. Angles are formed when two rays originate from the same endpoint, with the endpoint called the vertex and the rays the arms. There are different types of angles including acute, right, obtuse, straight, and reflex angles defined by their degree measurements. Adjacent angles have a common vertex and arm but different non-common arms. When a ray stands on a line, the sum of the two adjacent angles formed is 180 degrees, making them a linear pair.