Inscribed angles subtended by the same arc of a circle are equal.

Note in this slideshow the inscritbed angles are <DAC and <DBC. The endpoints DC are connected wiith arc DC. The inscribed angles share (are subtended by) arc DC. The interactive on the left allows you to change the vertex position for <DAC and <DBC. The size of the angle will not change when you move vertex A or B. Consider moving A so that it sits on top of B. The endpoints of the angles are also the same so the 2 angles are congruent. If you can remember what you see, you will likely remember: Inscribed angles subtended by the same arc of a circle are equal.

arc DC subtends inscribed angles A and B. Therefore <A = <B.

arc AB subtends inscribed angles C and D. Therefore <C = <D.

Interactive Activity

• Adjust the size of the inscribed angles by dragging the points A, B, C and D.
• Notice the red arc that connects the pair of angles subtended by that arc.
• <A will always equal <B and <C will always equal <D.
• Hold the SHIFT key when you drag on the circumference of the circle to change the size of the circle.