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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.