Question

A sector of a circle is a section shaped like a piece of pie, bounded by two radii and an arc. Which of the following conditions would always be satisfied if two sectors of the same circle were congruent?A. the arcs must be supplementaryB. The arcs must be complementaryC. The central angles must be complementary.D. The arcs must have the same measure E. the central angles must be supplementary F. the central angles must have the same measureG. the segments joining endpoints of each arc are congruentH. the segments joining the radius and arc must be identical.

Answer 1

For two sectors in the same circle to be congruent they have to have the same arc measure.

We will check each of the statements:

A. the arcs must be supplementary. FALSE

B. The arcs must be complementary. FALSE

C. The central angles must be complementary. FALSE

D. The arcs must have the same measure. TRUE

E. the central angles must be supplementary. FALSE

F. the central angles must have the same measure. TRUE

G. the segments joining endpoints of each arc are congruent. TRUE

H. the segments joining the radius and arc must be identical. ​FALSE