The concept of lines was introduced by ancient mathematicians, meant to represent straight objects with negligible width and depth. In geometry, lines and angles form the basic shapes. Lines are figures that are made up of infinite points that will always extend indefinitely in any direction. There are many types of lines such as intersecting lines, perpendicular lines, transversal lines, etc.
An angle is formed when two lines meet at a common point. The most practical shapes of mathematics are the geometrical shapes which are mostly taught in class 7. There are many types of angles: complementary angles, adjacent angles, vertically opposite angles, supplementary angles, etc.
The angles whose measures add up to 90 degrees are called complementary angles. These two angles need not be adjacent to be complementary. The complementary angles always appear in pairs. These angles can be part of the same or different figures.
The two angles that add up to 180 degrees are called supplementary angles. The supplementary angles always form a straight line when they meet at 180 degrees. These angles can either be adjacent or nonadjacent. The angles with the common vertex and common arm are called supplementary adjacent angles. Whereas the angles with different vertices and arms are called non-adjacent supplementary angles.
The angles which do not overlap and always have a common vertex and arm are called adjacent angles. Such angles share a common vertex but do not share a common side. The two adjacent angles can either be supplementary or complementary, based on their sum of value.
When the two lines intersect each other at a single point they form a linear pair of angles. After the intersection, if the angles are adjacent to each other are said to be linear. The sum of linear pair angles is always equal to 180 degrees.
The angles which are opposite each other are called vertically opposite angles. Such angles are opposite each other at a specific vertex. These angles are created by two intersecting lines and are also called vertical angles.
Two or more lines which intersect each other at a common point are called intersecting lines. The point where they intersect each other is known as the point of intersection.
When two lines intersect in the same plane at two distinct points it is called a transversal line. The intersection caused by a transversal line forms several angles. The transversal lines always connect the two parallel lines.
Through transversal lines, when two parallel lines intersect it forms eight angles such as corresponding angles, alternate exterior angles, alternate interior angles, and co-interior angles. When a transversal cuts the two or more lines, the angles which occupy the same relative position are the corresponding angles.
When the lines are parallel, the corresponding angles are congruent. If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent.
The lines which do not meet at any point in a plane and also do not intersect each other are called parallel lines. These lines have two starting points and an ending point.
The lines are said to be perpendicular when they form a right angle with each other and also meet at a single point. Such lines are opposite to each other.
In geometry, lines and angles have their properties which are based on points, vertices, arms, rays, etc.
A set of three or more points that lie on the same line are collinear points.
Non-collinear points do not lie on the same line.
The three points can be either collinear or non-collinear.
The collinear or non-collinear points do not lie together at the same line or point.
When two rays emerge from a common point it is called a vertex of angles.
The two rays forming the angle are called their sides or arms.
A reflex angle is formed when an angle is less than 360 degrees and greater than 180 degrees.
When two adjacent angles meet at 180 degrees is called a pair of angles.
Vertically opposite pairs of angles are formed when two lines intersect each other.