Question

circle o; \\( \angle a \\) intercepts \\( \widehat{bc} \\); \\( \angle d \\) intercepts \\( \widehat{bc} \\) \\( \angle a \cong \angle d \\) two statements are missing reasons. what reason can be used to justify both statements 2 and 3? third corollary to the inscribed angles theorem inscribed angles theorem central angle of a triangle has the same measure as its intercepted arc. \\( \angle \\) formed by a tangent and a chord is half the measure of the intercepted arc.

Explanation:

The inscribed angles theorem states that if two inscribed angles intercept the same arc, then the angles are congruent. In this case, \(\angle A\) and \(\angle D\) both intercept \(\overset{\frown}{BC}\). The third corollary is about angles in a semicircle, the central - angle statement is about central angles (not inscribed angles here), and the tangent - chord angle statement is for a different geometric situation (involving a tangent).

Answer:

inscribed angles theorem