AB is perpendicular to BC (given)
AB is perpendicular to BD (given)
So we have two right angles forming as indicated by the square angle markers in the diagram. All right angles are equal to 90 degrees (by definition). So angle ABC = angle ABD
We're given BC = BD. By the reflexive property we know that AB = AB (any segment is equal to itself).
So by the SAS congruence property, we can prove that triangle ABC is congruent to triangle ABD
Here's a further breakdown of how SAS works in this case
S: segment BC = segment BD
A: angle ABC = angle ABD
S: segment AB = segment AB