Part I: Measuring Arc Angle and Arc Length



MAED 391/591 Sketchpad Activity 2

Arcs & Chords

Part I: Measuring Arc Angle and Arc Length

1. Construct a circle. Construct two points on the circle.

2. Select the three points on the circle consecutively.

3. Measure the arc angle and the arc length. What is the meaning of these two measurements?

4. Connect the first and third points to the center of the circle with segments.

5. Measure this central angle.

6. What is the relationship between the measure of a central angle and the measure of the intercepted arc angle? Move the points on the circle around. Does your conjecture hold true? Write a theorem for this situation.

7. Construct a fourth point on the circle. Move this point so that it is not positioned on the same arc as the second point above.

8. Connect this fourth point to the first and third point with segment. Measure this angle.

9. What is the relationship between the measure of this inscribed angle and its intercepted arc? 10. Does this relationship hold if the vertex point and the other points are moved around the circle?

11. Write a theorem for this situation.

Part II: Diameters and Chords

Definition: A chord is a segment connecting two points on a circle. The minor (smaller) arc intercepted by a chord is called the arc of the chord.

1. Construct a circle. Construct a second point on the circle. Connect the two points on the circle with a segment.

2. Construct the midpoint of the chord.

3. Construct the perpendicular bisector of the chord.

4. What is the perpendicular bisector of a chord?

5. Measure the lengths of the segments of the bisected chord?

6. Measure the lengths of the segments of the perpendicular bisector of the chord.

7. Is there an relationship between the measurements in 5 and 6?

8. Are the any similar triangles present in the picture? How do you know? (Use what you discovered in Part I to help determine this)

9. Now try part 7 again!!

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