The diagram shows that <RTS ≅ <XTZ due to Segment Addition postulate . We are also know that RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯ and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯ because definition of a bisector . Because of these things, we know that △RTS≅ZTX by ASA . Finally we can prove RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ by CPCTC
Correct! Since <RTS ≅ <XTZ (given), RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯ (given), and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯ (given), we can conclude that △RTS≅△ZTX by the ASA (Angle-Side-Angle) congruence criterion.
Therefore, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we can say that RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯.