Consider \(\displaystyle\triangle{A}{D}{C}\)

and \(\displaystyle\triangle{A}{B}{C}\)

\(\displaystyle{A}{D}={A}{B}\) (Given)

\(\displaystyle{D}{C}={B}{C}\) (Given)

\(\displaystyle{A}{C}={A}{C}\) (reflexive property)

Step 2

By SSS congruency

\(\displaystyle\triangle{A}{D}{C}\stackrel{\sim}{=}\triangle{A}{B}{C}\)

\(\displaystyle\therefore\) the triangles must be congruenct.