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Geometry Geometer's Sketchpad Activity Angles and Arcs of a Circle Instructions: Complete the Geometer's Sketchpad activity found in this lesson. In this activity, you will create two sketches pertaining to central angles, inscribed angles and arc measurements of a circle. You will also be answering several analysis questions on this worksheet, which you will submit to your teacher. Be sure to save the Geometer’s Sketchpad file as instructed and submit the file to your teacher when you have completed the activity. Page 1: As you follow the Page 1 directions in the activity, complete the analysis question below. Follow steps 1-9, and then respond to question 1: 1. A. How do the measurements of central angle CAB and the measure of arc BC compare when point C is dragged around the circle? B. Fill in the blank to complete the conjecture about the measure of the central angle and the measure of the minor arc it intercepts: The measure of a central angle _______________the measure of its intercepted arc. C. Below is a circle with a center at point A. Use the circle to find the measurements listed. Arc DE = 40.05° E D Arc DC = 127.29° A 79.03° B C Measurement of minor arc CB = _________________ Measurement of angle CAD = ________________ Measurement of angle DAE = _______________ Measurement of minor arc EB = ______________ Measurement of angle EAB = ________________ Just remember that the sum of all angles in a circle should be 360o. Page 2: As you follow the Page 2 directions in the activity, complete the analysis question below. Follow steps 10-19, and then respond to question 2: 2. A. Drag point C so that the measurement of angle CBD is 60o; record the measurement of arc DC____________. B. Drag point C so that the measurement of angle CBD is 40o; record the measurement of arc DC____________. C. Drag point C so that the measurement of angle CBD is 115o; record the measurement of arc DC____________. D. Based on the measurements found in parts A-C fill in the blanks to complete the conjecture about the measure of an inscribed angle and the measure of the intercepted arc: The measure of an inscribed angle equals _______________ the measure of its intercepted arc. The measure of the intercepted arc is ______________ the measure of its inscribed angle. E. Use each circle to find the measurements listed. i. D A B measure of arc BC = 81.60° C Measurement of angle BAC = _______________ Measurement of angle BDC = _______________ ii. D A C B measure of arc BC = 44.16° Measure of angle BDC = ________________ iii. measure of angle BDC = 44.16° D A C B Measure of angle BAC = _______________ Measure of arc BC = __________________ Follow step 20. Submit the Geometer’s Sketchpad file and the student worksheet to your teacher.