This applet demonstrates the theorem of angles in the same segment.[br]You can use the slider to vary angle BCA, or drag points B, C, or D.
Angle BDA and angle BCA are angles subtended by the same arc, AB. [br]They are also angles in the same segment. [br]What do you notice about the two angles?
[math]\angle[/math]BDA and [math]\angle[/math]BCA are equal.
[math]\angle[/math]DEF and [math]\angle[/math]DGF are angles subtended by the same arc, DF.[br]They are also angles in the same segment.[br]Move the point D or F and observe the value of the two angles.
What do you notice about the values of angles DEF and DGF?
[math]\angle[/math]DEF and [math]\angle[/math]DGF are equal.
What can you say about angles in the same segment?
Angles in the same segment are equal.