Learning Resources

Investigation 4: Angles and Arcs

Complete the following activity to understand arc measures:

• Draw two circles, one with a radius of 6 cm, the other with a radius of 9 cm. Cut both circle out.
• Fold each circle in half, and then in half again. Open them up.
• What are the measures of the central angles in each circle? What is the ratio of one of the central angles to the complete circle?
• Examine an intercepted arc in each circle. Determine the ratio of each arc to the circumference of the circle.
• Lay the smaller circle on top of the larger circle such that the circles are concentric. What do you notice about the arc measures?
• Determine the relationship between the ratio of the intercepted arc to the circumference and the ratio of the central angle to the complete circle.
• The measure of each arc is 90⁰ . How does this compare to the corresponding central angle?