Can two triangles be proved congruent? If so, by which method, SSS, SAS, ASA, AAS, or HL?

SSS- Side – Side – Side method means if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

SAS – Side – Angle – side method meansif two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then triangles are congruent.

ASA - Angle – side – angle method means if two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, then triangles are congruent.

AAS – Angle – angle – side method if two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, then triangles are congruent.

HL – Hypotenuse – leg method means if the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, then two triangles are congruent.

First name the triangles in the given figure,

Here from the figure, $\overline{AB}\cong \overline{CD}$ and $m\angle A=m\angle C={90}^o$.

In $\Delta OAB\text{and}\Delta OCD$,

i. It is given that, $\overline{AB}\cong \overline{CD}$.

ii. It is given that, $m\angle A=m\angle C={90}^o$.

iii. And, $\angle AOB\cong \angle COD$(Vertical angles).

Therefore, $\Delta OAB\cong \Delta OCD$by AAS method.