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, $\stackrel{¯}{ED}â‰\dots \stackrel{¯}{EG}$and $\stackrel{¯}{DF}â‰\dots \stackrel{¯}{GC}$.

In $\mathrm{Δ}EFG\text{and}\mathrm{Δ}ECD$,

i. It is given that, $\stackrel{¯}{ED}â‰\dots \stackrel{¯}{EG}$ and $\stackrel{¯}{DF}â‰\dots \stackrel{¯}{GC}$.

ii. From (i), $\stackrel{¯}{ED}+\stackrel{¯}{DF}=\stackrel{¯}{EG}+\stackrel{¯}{GC}$, by Segment addition postulate, $\stackrel{¯}{EF}â‰\dots \stackrel{¯}{EC}$.

iii. By Reflexive Property, $\stackrel{¯}{E}â‰\dots \stackrel{¯}{E}$.

Yes, the above two triangles $\mathrm{Δ}EFGâ‰\dots \mathrm{Δ}ECD$ are congruent by SAS postulate.