Inscribed Angle Property
Definition

Inscribed angles subtended by the same arc are congruent (equal in measure).

Example

In the figures below, angleCAD and angleCBD are congruent (equal in measure), since both are inscribed angles subtended by arc(CD).

Inscribed Angle Property Example

In the figures above, angleACB and angleADB are congruent (equal in measure), since both are inscribed angles subtended by arc(AB).

Demonstration
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Explanation

Click here for an mathematical explanation of WHY the Inscribed Angle Property works.

Note that this is not a PROOF but an EXPLANATION.