The figure shows a circle with center O and two congruent chords AB and CD. To prove that the chords are equidistant from the center, it has to be proved that segment OS is congruent to segment OT.

Which of these is a step that can be used in the proof?

Question

The figure shows a circle with center O and two congruent chords AB and CD. To prove that the chords are equidistant from the center, it has to be proved that segment OS is congruent to segment OT.



Which of these is a step that can be used in the proof?

anonymous · Answer

Statement: Segment OS is congruent to segment OT.
   Reason: Radii of the same circle are congruent.

 Statement: Segment OS is congruent to segment SD.
   Reason: Congruent sides of isosceles triangle OSD.

 Statement: Triangle ODS is congruent to triangle OBT.
   Reason: ASA triangle congruency principle.

 Statement: Segment OS is congruent to segment OT.
       Reason: Corresponding parts of congruent triangles are congruent.