Lines and Angles
A point is dimensionless. A line is a one-dimensional figure that has no thickness and which extends infinitely in both the directions. A line segment is a part of a line whose both ends are fixed. A ray is a part of a line whose one end is fixed. An angle is formed when two lines, line segments or rays intersect at a point. Angles can be categorized as acute angle, right angle, obtuse angle, straight angle and reflex angle. When the sum of the measures of two angles is 90°, then the angles are called complementary angles. When the sum of the measures of the two angles is 180°, then the angles are called supplementary angles.
Two angles are adjacent, if they have a common vertex, a common arm and their non-common arms are on different sides of the common side. A pair of adjacent angles, whose non-common sides lie opposite to each other at an angle of 180°, is called a linear pair. A pair of non-adjacent angles formed by the intersection of two straight lines is called vertically opposite angles. Vertically opposite angles are equal.
Parallel lines are coplanar and they do not intersect each other. Transversal intersects two or more lines.
If a transversal intersects a pair of parallel lines, then
pair of vertically opposite angles is equal.
pair of alternate angles is equal.
consecutive interior angles are supplementary.
corresponding angles are equal.
If a transversal intersects two lines then the lines are parallel when:
any one pair of corresponding angles is equal, or
any one pair of alternate interior angles is equal, or
any one pair of interior angles on the same side of the transversal is supplementary.
Lines which are parallel to a given line are parallel to each other.
The sum of the three angles of a triangle is 180°. If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.
Keywords: Intersecting lines, Non-intersecting lines, Collinear points, Non-collinear points