91Ó°ÊÓ

Consider$\mathrm{Δ}AGB$ and $\mathrm{Δ}AFE$. From the given information it can be observed that $∠1â‰\dots ∠2$,$\stackrel{¯}{AG}â‰\dots \stackrel{¯}{AF}$ as they are the opposite sides to the angles$∠3\text{and}∠4$ also,$∠7â‰\dots ∠8$ then by SAS postulate, $\mathrm{Δ}AGBâ‰\dots \mathrm{Δ}AFE$.

As$\mathrm{Δ}AGBâ‰\dots \mathrm{Δ}AFE$ then by corresponding parts of congruent triangles $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AE}$.

Consider $\mathrm{Δ}ABC$and $\mathrm{Δ}AED$. From the given figure it can be observed that $\stackrel{¯}{AC}â‰\dots \stackrel{¯}{AD}$as they are the opposite sides to the angles $∠5\text{and}∠6$,$∠1â‰\dots ∠2$ and$\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AE}$ then by SAS postulate, $\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}AED$.

As$\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}AED$ then by corresponding parts of congruent triangles, $\stackrel{¯}{BC}â‰\dots \stackrel{¯}{ED}$.

$\mathrm{Δ}AGBâ‰\dots \mathrm{Δ}AFE$ by SAS postulate then by corresponding parts of congruent triangles $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AE}$.$\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}AED$ by SAS postulate then corresponding parts of congruent triangles, $\stackrel{¯}{BC}â‰\dots \stackrel{¯}{ED}$.