Angles related to Parallel Lines and Transversals

8.3

Angles related to Parallel Lines and Transversals

Parallel lines:

Definition

Parallel lines will not intersect with each other.
Parallel lines can be denoted using arrowheads as shown in the diagram below.

Transversal:

Definition

A straight line that intersects two or more straight lines.
The diagram below shows that \(PQ\) is a transversal.

The corresponding angles, alternate angles and interior angles:

(i) Corresponding angles

The corresponding angles are equal where \(\angle a=\angle b\).

(ii) Alternate angles

The alternate angles are equal where \(\angle b=\angle c\).

(iii) Interior angles

The sum of the interior angles is \(180^\circ\) where \(\angle c+\angle d=180^\circ\).

Angles of elevation and depression:

(i) Angle of elevation

Definition

When a person sees an object which is at a higher level, the angle between the line of sight and the horizontal line is known as the angle of elevation.

Form the diagram above, angle \(a\) is the angle of elevation of the bird from the sight of the boy.

(ii) Angle of Depression

Definition

When a person sees an object which is at a lower level, the angle between the line of sight and the horizontal line is known as the angle of depression.

Form the diagram above, angle \(b\) is the angle of depression of the cat from the sight of the girl.