Inscribed Angle Theorem (Corollary 2) (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.) Click on the first pink checkbox to show just 1 inscribed angle that intercepts arc AB. Notice, in the applet below, how the inscribed angle and central angle (angle AOB) both intercept the same arc. Use the inscribed angle theorem you've just learned (from http://tube.geogebra.org/m/1473237) help you see a second corollary that easily provable from this theorem. Be sure to move points A, B, and the pink vertices of all the inscribed angles you see around as well. (You can also change the radius of the circle if you wish.) Complete the following corollary: In a circle, if 2 or more inscribed angles intercept the SAME ARC, then...
Activity & question are contained in the description above the applet.