In this video I go over some very interesting and useful corollary properties that stem from the inscribed value theorem videos that I covered in my earlier videos. Basically from the fact that the central angle of any circle is constant then the inscribed angles on both the major arc and minor arc that are subtended from the same 2 points as that of the central angle are always constant. This fact greatly simplifies the process of finding angles of triangles and other shapes so it is very important to understand these topics and the inscribed angle theorem as a whole!
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Inscribed Angle Theorem: Corollary Properties
Recap from my earlier videos:
The Inscribed Angle Theorem (or Central Angle Theorem):
The inscribed angle subtended on the major arc of two given points on the circle is half of that of the central angle which subtends on the same arc on the circle.
Also recall from my earlier video that the angle subtended on the minor arc is supplementary to half the central angle:
Supplementary Angles: Two angles are supplementary if they add up to 180 degrees.
Corollary 1: The angle subtended on the major arc is constant.
Corollary 2: The angle subtended on the minor arc is constant and supplementary to that of the major arc.
These corollaries follow from the fact that the central angle is constant and thus regardless of where the inscribed angles are subtended they are constant because of their relation relative to the constant central angle.
