If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice-versa. This property is called as the Linear pair axiom. If two lines intersect each other, then the vertically opposite angles are equal.
If a transversal intersects two parallel lines, then
- each pair of corresponding angles is equal
- each pair of alternate interior angles is equal
- each pair of interior angles on the same side of the transversal is supplementary
If a transversal intersects two lines such that, either (i) any one pair of corresponding angles is equal, or (ii) any one pair of alternate interior angles is equal, or (iii) any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.
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.