Given data:
QP = PT and RP = SP
Let us first prove ΔQPR and ΔSPT are congruent.
In ΔQPR and ΔSPT,
QP ≅ TP (Given side)
∠QPR ≅ ∠ SPT (Vertically opposite angles are congruent)
RP ≅ SP (Given side)
Therefore, ΔQPR ≅ ΔSPT (by SAS congruence rule)
By corresponding parts of congruence triangles are congruence,
⇒ ∠Q ≅ ∠T
Hence ∠Q ≅ ∠T.
