The diagram shows that <RTS ≅ <XTZ due to . We are also know that RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯ and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯ because . Because of these things, we know that △RTS≅ZTX by . Finally we can prove RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ by

Question

The diagram shows that <RTS ≅ <XTZ due to . We are also know that RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯ and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯ because . Because of these things, we know that △RTS≅ZTX by . Finally we can prove RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ by

Answer 1

the Side-Angle-Side (SAS) congruence theorem.

(Explanation: In the triangle RTS, we know that angle RTS is congruent to angle XTZ because they are shown to be equal in the diagram. Additionally, we know that side RT is congruent to side ZT, and side ST is congruent to side XT because they are given in the problem. Therefore, we have enough information to conclude that triangle RTS is congruent to triangle ZTX using the SAS congruence theorem. Since these triangles are congruent, we can then conclude that side RS is congruent to side XZ based on corresponding parts of congruent triangles.)