Question

In the adjacent figure $△ABC$ and $△DBC$ are two triangles such that $\overline{AB}=\overline{BD}$ and $\overline{AC}=\overline{CD}$. Show that $△ABC\cong △DBC$

Answer 1

Given ; $\Delta ABC$ and $\Delta DBC$ are two triangles such that $AB=BD$ and $AC=CD$.

To show, $\Delta ABC\cong \Delta DBC$

proof;

in triangle $DBM$ and triangle $AMC$,

$AB=BC$ (Given)

$AC=CD$ (Givne)

$BC=BC$ ( Common )

Therefore, by $SSS$ criterion of congruency, triangle $ABC$ is congruent to triangle $DBC$.