INVESTIGATIONS
Try the following investigations using either traditional construction tools (compass and straightedge) or Geometer's Sketchpad.
Investigation #1: Construct a large circle. Select two points on the circle. Label them A and B. Select a point P on the major arc and construct inscribed angle APB. With your protractor, measure angle APB. Select another point Q on major arc APB and construct inscribed angle AQB. Measure angle AQB. How does the measure of angle AQB compare with the measure of angle APB?
Repeat the investigation with points P and Q selected on a minor arc AB. State your observations as a conjecture.
Investigation #2: Construct a large circle. Construct a diameter. Inscribe three angles in the same semicircle. Measure each angle with your protractor. Compare your results with others in the class and make a conjecture.
Investigation #3: Construct a large circle. Construct an inscribed quadrilateral. Measure each of the four inscribed angles. Write the measure of each angle. Compare you observations with other in the class. State your observations as a conjecture.
Use conjectures that you formed in the investigations in this lesson and theorems to solve the following problems:
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