We can prove that ∆ABD and ∆CBD congruent by the SSS Postulate.
The SSS postulate states that of three sides in one triangle are congruent to three corresponding sides in another, therefore, the two triangles are congruent.
From the diagram shown,
AB ≅ CB,
AD ≅ CD
BD = BD
We have three sides in ∆ABD that are congruent to three corresponding sides in ∆CBD.
