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, $\stackrel{¯}{BC}â‰\dots \stackrel{¯}{BD}$and $\stackrel{¯}{AC}â‰\dots \stackrel{¯}{AD}$.

In $\mathrm{Δ}ABC\text{and}\mathrm{Δ}ABD$,

i. It is given that, $\stackrel{¯}{BC}â‰\dots \stackrel{¯}{BD}$.

ii. Also it is given that, $\stackrel{¯}{AC}â‰\dots \stackrel{¯}{AD}$.

iii. By Reflexive property, $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AB}$.

Yes, the above two triangles $\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}ABD$ are congruent by SSS postulate.