Show that tetrahedral has a segment perpendicular to a plane ![enter image description here]( In this tetrahedral, I have that $$DC = DA, AB = BC$$ and also, I have that angle $DBA$ is $90^\circ$. I need to show ...--prophetes.ai

Show that tetrahedral has a segment perpendicular to a plane ![enter image description here]( In this tetrahedral, I have that $$DC = DA, AB = BC$$ and also, I have that angle $DBA$ is $90^\circ$. I need to show that at least one segment is perpendicular to a plane in this tetrahedral. What I tried: We're using the theorem that says that if a segment is perpendicular to 2 segments, then it's perpendicular to the plane defined by these two segments. Therefore, since I think that $DB$ is perpendicular to the plane $ABC$, I just need to show that $DB$ is perpendicular to $BC$, then we have the $2$ lines necessary to prove. I think I can use some property of similarity, since we have that triangle $DCA$ and $ABC$ are similar (LLL). Any help?

Try instead showing that $\triangle DBA$ and $\triangle DBC$ are congruent.