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Inscribed Angle Theorem: Take 4!


In the GeoGebra applet below: 1) Use the SEGMENT Toolbar Image tool to construct segments , , , and . 2) Use the ANGLE Toolbar Image tool to measure and display the measure of and . Then, answer the questions that appear below the applet.


Immediately select the MOVE Toolbar Image arrow. Then drag the angle measures to a place where you can see them clearly. What do you IMMEDIATELY NOTICE? Describe in detail in the space provided.


Now drag the BLUE DOT on the blue slider to change the measure of the circle's blue central angle. (You can also enter any angle measure you wish). Each gray angle is said to be an inscribed angle of this circle. Note that each gray inscribed angle intercepts the same arc (of the circle) as the blue central angle. What do you notice about the measures of the gray inscribed angles with respect to the measure of this blue central angle?