  We construct spectral triples on C*-algebraic extensions of unital
C*-algebras by stable ideals satisfying a certain Toeplitz type property using
given spectral triples on the quotient and ideal. Our construction behaves well
with respect to summability and produces new spectral quantum metric spaces out
of given ones. Using our construction we find new spectral triples on the
quantum 2- and 3-spheres giving a new perspective on these algebras in
noncommutative geometry.
