In triangles, ABD and ACE,
angle BAD in triangle ABD = angle CAE in triangle ACE -----(1)
angle BDA in triangle ABD = angle AEC in triangle ACE (90) ----(2)
Therefore other angles of these triangles are equal.
Hence all angles of triangles ABD and ACE are equal,
hence triangles ABD and ACE are similar.
Therefore corresponding sides are proportional.
Hence AB / AC = AD / AE OR ABxAE = ACxAD