91Ó°ÊÓ

If two angles of triangle are congruent then the sides opposite to those angles are congruent.

It is given that,$∠ACBâ‰\dots ∠ABC$. Therefore, by converse isosceles triangle theorem,$\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AC}$.

If two angles of triangle are congruent then the sides opposite to those angles are congruent.

It is given that,$∠DCBâ‰\dots ∠DBC$. Therefore, by converse isosceles triangle theorem,$\stackrel{¯}{DB}â‰\dots \stackrel{¯}{DC}$.

Reflexive property states that, $\stackrel{¯}{PQ}â‰\dots \stackrel{¯}{PQ}$. Therefore, in this case by reflexive property, $\stackrel{¯}{AD}â‰\dots \stackrel{¯}{AD}$.

If three sides of one triangle are congruent to three sides of other triangle then the triangles are congruent.

Here, $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AC}$, $\stackrel{¯}{DB}â‰\dots \stackrel{¯}{DC}$and $\stackrel{¯}{AD}â‰\dots \stackrel{¯}{AD}$then by $SSS$postulate $\mathrm{Δ}ACDâ‰\dots \mathrm{Δ}ABD$.

Therefore, a pair of congruent triangles is$\mathrm{Δ}ACD$and $\mathrm{Δ}ABD$.