Geometry
Activity:
Angles and Arcs
Posted on May 12, 2008
Topic: Circles
In this activity, students will explore angles constructed in a circle and how their measures are related to the measures of the intercepted arcs. Then students will explore a figure which has an angle vertex either inside the circle (angles formed by chords) or outside the circle (angles formed by secants).
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Activity Key Steps:
In problem 1, students explore inscribed and central angles. They will see a central angle AOB has been constructed and measured. The central angle measure is used as the arc measure. Students construct a point labeled C and construct two segments AC and BC.
They will realize that the measure of the arc is twice that of the measure of ACB. They use the manual data capture to record the measurements in a spreadsheet.
Students construct another point and label it D. They then label the new angle ADB. Students should observe that angles ACB and ADB have the same measurement.
In problem 2, students investigate angles with vertices inside or outside a circle. In the circle are chords WY and XZ that intersect each other at point P. The intercepted arcs WX and YZ are measured.
They will see that when P is inside the circle the measure of angle YPZ is half of the sum of the arcs. When P is outside the circle the measure of angle YPZ is half of the difference of the arcs.
At the end of this activity, students will be able to construct central and inscribed angles, angle vertices inside and outside a circle. They will also be able state the relationship of angles and intercepted arcs.