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?

Answer 1

Statement: Segment OS is congruent to segment OT.
Reason: Radii of the same circle are congruent.

Statement: Angle OSD is congruent to angle OTB.
Reason: All right angles are congruent.

Statement: Angle OSD is congruent to angle OTB.
Reason: Corresponding angles of congruent triangles are congruent.

Statement: Angle SOD is congruent to angle TOB.
Reason: Vertically opposite angles are congruent.

Answer 2

clearly its not first one as OS is not a radius

Answer 3

Right.

Answer 4

second statement is true. as OSD & OTB are right angles, as OS & OT is the distance from center to chord <===== save this

Answer 5

Ohhh I dont think I ever wouldve figured that out..

Answer 6

third statement is also true. but the reason is wrong -- actually its reverse. since the angles are congruent, we use it for proving triangles are congruent. so this is WRONG reason. throw it

Answer 7

like I said, never can figure this stuff out.

Answer 8

fourth statement is correct. reason is wrong. as they are not vertically opposite angles...

its okay... :) now you see it :)