deleted

2.
since AP=BQ=CR
ABCD is a square
so PB=QC
angle PBQ=angle QCR
so triangle PBQ is congruent to triangle QCR
so PQ =QR
so PQR is an isos. triangle

1.

a. Triangle QXY is similar to triangle QPR;
=> angle QXY = angle QPR, thus XY // PR

also, triangle AXY is similar to triangle ABC;
=> angle AXY = angle ABC, thus XY // BC

PR // XY // BC and hence the result.