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Read Me - Inscribed Angles in Circles Instructions (Word Format) (46.0K)

Laboratory Investigation 9.2

1. Draw a circle and select any 2 points A and B on its circumference which are not the endpoints of a diameter (see figure). Then select a different point V on the circumference and draw AVB. This is called an inscribed angle because the vertex of the angle is on the circle and and are chords of the circle. What can be said about the measure of such angles as point V moves to different locations on the circumference and points A and B remain fixed?
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2. A central angle of a circle has its vertex at the center of the circle, as shown in the following figure.
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a. Draw a circle and select any 2 points A and B on the circumference. Label the center of the circle as O and draw central AOB. Select point V on the circumference and draw inscribed AVB. How does the measure of inscribed AVB compare to the measure of central AOB? Repeat such measurements for other inscribed angles and their corresponding central angles. Is there a relationship? Form a conjecture and test it on other angles.
b. Draw a circle and label the endpoints of a diameter as A and B. Select a point V on the circumference which is different from points A and B and measure AVB. Form a conjecture about AVB as point V moves about the circumference.
3. Draw a circle and select any 4 point on the circumference as the vertices of a quadrilateral. Measure the pairs of opposite angles of the quadrilateral and look for relationships. Move the vertices on the circle to see if your relationships hold. Will such relationships hold for an arbitrary quadrilateral whose vertices are not on the circumference of a circle?
*This investigation may be carried out with software such as Cabri Geometry II, Geometer's Sketch Pad, or The Geometric Super Supposer.