Question

ircle D is shown with the measures of the minor arcs.

Circle D is shown. Line segments D E, D F, D G, and D H are radii. Lines are drawn to connect the points on the circle and to create secants E F, F G, G H, and H E. The measure of arc E F is 115 degrees, the measure of arc F G is 115 degrees, the measure of arc G H is 65 degrees, and the measure of arc H E is 65 degrees.

Which segments are congruent?

EH and EF
GH and FE
FG and EH
EF and GF

Answer 1

EF and GF.

They subtend equal arcs (arc EF = arc FG = 115°), so the corresponding chords EF and FG are congruent.