91Ó°ÊÓ

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, $\stackrel{¯}{AO}â‰\dots \stackrel{¯}{CO}$ and $\stackrel{¯}{AB}\left|\right|\stackrel{¯}{DC}$.

Now,

In $\mathrm{Δ}OAB\text{and}\mathrm{Δ}OCD$

$\stackrel{¯}{AO}â‰\dots \stackrel{¯}{CO}$(given)

$∠AOBâ‰\dots ∠COD$(Vertical angles since \[\overline{AB}||\overline{DC}\])

Also,

$∠OABâ‰\dots ∠OCD\text{and}∠OBAâ‰\dots ∠ODC$(Alternate angles)

As per the definitions of method ASA and AAA, $\mathrm{Δ}OABâ‰\dots \mathrm{Δ}OCD$.

Therefore,$\mathrm{Δ}OABâ‰\dots \mathrm{Δ}OCD$ by ASA and AAA method.