Which theorem states that angles in the same segment of a circle are equal?

The theorem that states that angles in the same segment of a circle are equal is known as the Angles in the Same Segment theorem. This theorem is crucial in understanding the properties of circles and their associated angles. The concept is based on the geometric fact that if you have a circle and a segment created by drawing a chord, any angle formed by two lines drawn from the ends of this chord to any point on the arc will be equal if the point lies on the same segment of the circle.

For example, if you have points A and B on the circumference of the circle and a point C somewhere on the arc of circle between A and B, the angles CAB and CDB (where D is another point on the circle arc) will be equal because they span the same arc AB. This consistency is valuable for proving various properties and solving problems relating to circle geometry.

The significance of this theorem is that it allows for the derivation of other properties in circle theorems and can be applied in various geometrical proofs and constructions. Understanding this theorem enables deeper insight into the relationships between angles and arcs in circle geometry.