Respuesta :

Good evening ,

Step-by-step explanation:

Using Pythagorean theorem in both right triangles PRQ and PRS we can prove that segment RQ ≅ segment RS

then R is a point of the mediator of segment QS

and since PQ = PS then P also is a point of the mediator of segment QS

finally line PR is the mediator of the segment QS

therefore the line PR passes through the midpoint of segment QS.

:)