Definition:Segment of Circle

As Euclid defined it:

"A segment of a circle is the figure contained by a straight line and a circumference of a circle."

Base
The base of a segment is the straight line forming one of the boundaries of the seqment.

Angle of a Segment
As Euclid defined it:

"An angle of a segment is that contained by a straight line and a circumference of a circle."

That is, it is the angle the base makes with the circumference where they meet.

Angle in a Segment
As Euclid defined it:

"An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined."

Similar
As Euclid defined it:

"Similar segments of circles are those which admit equal angles, or in which the angles are equal to one another."