Question

Prove: angles inscribed in the same arc are congruent

Answer 1

Construct a circle.  Label its center P. 

2.     Use a straightedge to construct a central angle. Label it .

3.     Locate three points on Circle P in the exterior of  and label them T, U, and V.  Use a straightedge to draw the inscribed angles ., and.

 

Investigate:

4.     Use a protractor to measure , , , and.  Make a table similar to the one below.  Record the angle measures for Circle 1 in the table. 

5.     Repeat Steps 1 through 3 using different central angles.  Record the measures in your table. 

 

Make a Conjecture:

6.     Use the results in your table to make a conjecture about how the measure of an inscribed angle is related to the measure of the corresponding central angle. 

 

An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.  The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle.