Inscribed Angles and Three Corollaries

In honor of March Madness, I decided to base my Geometry Hunters post on basketball. While playing basketball at Oakwood one day, I looked up to notice the ring part of the hoop was a perfect example of a circle. I then went on to try to prove the three corollaries listed in Chapter 9 of our textbooks with this simple real-life example of a circle.

Corollary 1: If two inscribed angles intercept the same arc, then the angles are congruent.

Corollary 2:  An angle inscribed in a semicircle is a right angle.

And finally,

Corollary 3: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. 

(~RO5)