[PQRS is s square.]
[From Step 1.]
All four angles of a square are equal to 90°. The diagonals of the square bisect its angles.
⇒ ∠OQP = ∠OPQ = ∠OQR = ∠ORQ = ∠ORS = ∠OSR = ∠OSP = ∠OPS = 45°
∠QRT = ∠QTR = 45°
[∠RQT = 90° and = .]
bisects ∠RQT. So, ∠UQR = ∠UQT = 45°
[U is the midpoint of line segment RT.]
If two angles and included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Therefore, ΔOPQ ≅ ΔOQR ≅ ΔORS ≅ ΔOSP ≅ ΔURQ ≅ ΔUQT.