Question

In a triangle ABC , D is mid - point of BC ; AD is produced upto E so that DE = AD prove that :
$$ \Delta ABD$$ and $$\Delta ECD$$ are congruent

Answer 1

Given ; A $$ \Delta ABC $$ in which D is the mid - point of BC
AD is produce to E so that DE = AD
We need to prove that
$$\Delta ABD \cong \Delta ECD $$
AB = EC
AB \\ EC
In $$ \Delta ABD$$ and $$\Delta ECD $$
BD = DE [D is the midpoint of BC]
$$ \angle ADB = \angle CDE $$ [Vertically opposite angles]
AD = DE [Given]
By Side - Angle - Side criterion of congruence we have
$$ \Delta ABD \cong \Delta ECD $$