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Student Lesson Summary
We’ve been using compasses this year to draw circles. They work because of the precise de nition of a circle. The point of the compass is placed at the center of the circle and the pencil traces out all points that are some xed distance, the radius, from the center.
Just as we could draw a part of a line to form a line segment between 2 points, we can also draw a part of a circle to form an arc between 2 points.
Every point on the arc is the same distance from the center, . Just as we could measure the circumference of an entire circle centered at , we can measure the arc length of just that portion that lies on the arc .
We can see a connection between the arc length of and the angle . The greater the angle , the greater the arc length of .
The region inside a circle bounded by a central angle and its arc is called a sector. The greater the angle, the greater the area of the sector as well.
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Teacher Guide
