Which theorem or postulate can be used to prove Delta RPQ De

Which theorem or postulate can be used to prove Delta RPQ Delta RST? Given R is the midpoint of QT and QT bisects PS at R. SSS SSA SAS There is not enough information to prove these triangles are congruent.

Solution

Given R is the midpoint of QT and QT bisects PS at R means that R is mid point of QT as well as PS. So, QR would be equal to RT and PR would be equal to RS

Hence in triangles RPQ and RST,

QR =RT

PR =RS

and angle QRP = angle SRT (Vertically opposite angles).

The two triangles would thus be congruent by SAS.