Inscribed Angle Theorem (Corollary 1) (Proof without Words)
- Tim Brzezinski
Recall that the measure of an arc of a circle is the same as the measure of its corresponding central angle. (See applet.) In this applet, the central angle always remains a straight angle (180 degrees). Thus, the intercepted arc is a semicircle. Click on the pink checkbox to show the inscribed angle. Notice how the inscribed angle and central angle both intercept the same arc. Use the inscribed angle theorem you've just learned (from http://tube.geogebra.org/m/1473237) to make a conjecture as to what the measure of the inscribed angle in this applet should be. Be sure to move points B, C, and the pink vertex of the inscribed angle around as well. (You can also change the radius of the circle if you wish.) Complete the following corollary: An inscribed angle that intercepts a semicircle is always.....
Key directions and questions are in the description above the applet.