Line Segment: A line that has two endpoints is called a line segment.
Ray: A ray has one end point and infinitely extends in one direction.
Obtuse angle: The angle that is between 90° and 180° is an obtuse angle, ∠B as shown below.
Right angle: The angle that is 90° is a Right angle, ∠C as shown below.
Straight angle: The angle that is 180° is a straight angle, ∠AOB in the figure below.
Supplementary angles:
In the figure above, ∠AOC + ∠COB = ∠AOB = 180°
If the sum of two angles is 180° then the angles are called supplementary angles.
Two right angles always supplement each other.
The pair of adjacent angles whose sum is a straight angle is called a linear pair.
Complementary angles:
∠COA + ∠AOB = 90°
If the sum of two angles is 90° then the two angles are called complementary angles.
Adjacent angles:
The angles that have a common arm and a common vertex are called adjacent angles.
In the figure above, ∠BOA and ∠AOC are adjacent angles. Their common arm is OA and common vertex is ‘O’.
Vertically opposite angles:
When two lines intersect, the angles formed opposite to each other at the point of intersection (vertex) are called vertically opposite angles.
In the figure above,
x and y are two intersecting lines.
∠A and ∠C make one pair of vertically opposite angles and
∠B and ∠D make another pair of vertically opposite angles.
Perpendicular lines: When there is a right angle between two lines, the lines are said to be perpendicular to each other.
Here, the lines OA and OB are said to be perpendicular to each other.
Parallel lines:
Here, A and B are two parallel lines, intersected by a line p.
The line p is called a transversal, that which intersects two or more lines (not necessarily parallel lines) at distinct points.
As seen in the figure above, when a transversal intersects two lines, 8 angles are formed.
Let us consider the details in a tabular form for easy reference.
| Types of Angles | Angles |
| Interior Angles | ∠3, ∠4, ∠5, ∠6 |
| Exterior Angles | ∠1, ∠2, ∠7, ∠8 |
| Vertically opposite Angles | (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8) |
| Corresponding Angles | (∠1, ∠5), (∠2, ∠6), (∠3, ∠7), (∠4, ∠8) |
| Interior Alternate Angles | (∠3, ∠5), (∠4, ∠6) |
| Exterior Alternate Angles | (∠1, ∠7), (∠2, ∠8) |
| Interior Angles on the same side of transversal | (∠3, ∠6), (∠4, ∠5) |
When a transversal intersects two parallel lines,
- The corresponding angles are equal.
- The vertically opposite angles are equal.
- The alternate interior angles are equal.
- The alternate exterior angles are equal.
- The pair of interior angles on the same side of the transversal is supplementary.
We can say that the lines are parallel if we can verify at least one of the aforementioned conditions.