Definitions and properties

Here are some basic definitions and properties of lines and angles in geometry:

Line segment: A line segment has two end points with a definite length.

Ray: A ray has one end point and infinitely extends in one direction.

Straight line: A straight line has neither starting nor end point and is of infinite length.



Acute angle: The angle that is between 0° and 90° is an acute angle, ∠A in the figure below.

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.