Objective:

To verify that the angles in the same segment of a circle are equal.

Basic Concepts and Facts:

Segments of a Circle :

• A chord of a circle divides the circle into two regions,called the segments of the circle.
• The minor segment is the region bounded by the chord and the minor arc intercepted by the chord.
• The major segment is the region bounded by the chord and the major arc intercepted by the chord.

Angles in Different Segments :
 

In the following diagram, ∠APB is in the major segment and ∠AQB is in the minor segment. So,   we say that ∠APB and ∠AQB are in different segments.

Angles in the Same Segment :

In the following diagram, ∠PRQ and ∠PSQ are in the major segment. So, we say that ∠PRQ  and ∠PSQ are in the same segment.