PROPERTIES OF CIRCLES

Open Investigation 7.4CENTRAL ANGLES, ARCS, AND CHORDSStep 1:Take one of your patty papers with a circleon it and fold a central angle. (You may needto find the center of the circle first.)Step 2:Step 3:Use another patty paper to trace the central angle. Then retrace the angle in the originalcircle so that you have two central angles (that are not vertical angles) with the samemeasure. (It will be easier to do the investigation if the two angles do not overlap.)Fold or trace to compare the lengths of the intercepted arcs and the chords of the twocentral angles.Step 4: Repeat steps 1-3 with another pair of congruent central angles.Compare your results with the results of others near you. Write a conjecture about the lengths of theintercepted arcs and chords of two congruent central angles.~47Open Investigation 7.5INSCRIBED ANGLESStep 1:Take one of your patty papers with a circleon it and fold or draw an inscribed angle.Step 2:Step 3:Fold or draw a central angle intercepting the same arc as the inscribed angle.Compare the measures of the central angle and the inscribed angle.Compare your results with the results of others near you. Write a conjecture about the relationshipbetween the measures of an inscribed angle and the central angle intercepting the same arc.~48PROPERTIES OF CIRClfS 11 7